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ABSTRACT
DISCRETE ELEMENT METHOD BASED SCALE-UP MODEL FOR
MATERIAL SYNTHESIS USING BALL MILLING
by
Priya Radhi Santhanam
Mechanical milling is a widely used technique for powder processing in various areas. In
this work, a scale-up model for describing this ball milling process is developed. The
thesis is a combination of experimental and modeling efforts.
Initially, Discrete Element Model (DEM) is used to describe energy transfer from
milling tools to the milled powder for shaker, planetary, and attritor mills. The rolling and
static friction coefficients are determined experimentally. Computations predict a quasi-
steady rate of energy dissipation, Ed, for each experimental configuration. It is proposed
that the milling dose defined as a product of Ed and milling time, t, divided by the mass of
milled powder, mp characterizes the milling progress independently of the milling device
or milling conditions used. Once the milling dose is determined for one experimental
configuration, it can be used to predict the milling time required to prepare the same
material in any milling configuration, for which Ed is calculated. The concept is validated
experimentally for DEM describing planetary and shaker mills. For attritor, the predicted
Ed includes substantial contribution from milling tool interaction events with abnormally
high forces (>103 N). The energy in such events is likely dissipated to heat or plastically
deform milling tools rather than refine material. Indeed, DEM predictions for the attritor
correlate with experiments when such events are ignored in the analysis.
With an objective of obtaining real-time indicators of milling progress, power,
torque, and rotation speed of the impeller of an attritor mill are measured during
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preparation of metal matrix composite powders in the subsequent portion of this thesis.
Two material systems are selected and comparisons made between in-situ parameters and
experimental milling progress indicators. It is established that real-time measurements
can certainly be used to describe milling progress. However, they need to be interpreted
carefully depending on hardness of brittle component relative to milling media.
To improve the DEM model of the attritor mill, it is desired to avoid the removal
of unrealistic, high-force events using an approach that would not predict such events in
the first place. It is observed that during experiments in attritor, balls may jam causing an
increased resistance to the impeller’s rotation. The impeller may instantaneously slow
down, quickly returning to its pre-set rotation rate. Previous DEM models did not
account for such rapid changes in the impeller’s rotation. In this work, this relationship
between impeller’s torque and rotation rate is obtained experimentally and introduced in
DEM. As a result, predicted Ed, are shown to correlate well with the experimental data.
Finally, a methodology is proposed combining an experiment and its DEM
description enabling one to identify the appropriate interaction parameters for powder
systems. The experiment uses a miniature vibrating hopper and can be applied to
characterize the powder flow for variety of materials. The hopper is designed to hold up
to 20,000 particles of 50-µm diameter, which can be directly described in DEM. Based
on comparison of discharge rate from experiments and model, all 6 interaction
parameters were analyzed and the ideal conditions identified for Zirconia beads. The
values of these parameters for powders are generally not the same as those established for
macroscopic bodies. In addition, effects of some other experimental parameters such as
particle size distribution and amplitude of vibration are also investigated.
DISCRETE ELEMENT METHOD BASED SCALE-UP MODEL FOR
MATERIAL SYNTHESIS USING BALL MILLING
by
Priya Radhi Santhanam
A Dissertation
Submitted to the Faculty of
New Jersey Institute of Technology
in Partial Fulfillment of the Requirements for the Degree of
Doctor of Philosophy in Chemical Engineering
Otto H. York Department of
Chemical, Biological and Pharmaceutical Engineering
January 2014
Copyright © 2013 by Priya Radhi Santhanam
ALL RIGHTS RESERVED
APPROVAL PAGE
DISCRETE ELEMENT METHOD BASED SCALE-UP MODEL FOR
MATERIAL SYNTHESIS USING BALL MILLING
Priya Radhi Santhanam
Dr. Edward L. Dreizin, Dissertation Advisor Date
Professor of Chemical, Biological and Pharmaceutical Engineering, NJIT
Dr. Rajesh N. Davé, Committee Member Date
Distinguished Professor of Chemical, Biological and Pharmaceutical Engineering, NJIT
Dr. Mirko Schoenitz, Committee Member Date
Research Associate Professor of Chemical, Biological and Pharmaceutical Engineering,
NJIT
Dr. Ecevit A. Bilgili, Committee Member Date
Assistant Professor of Chemical, Biological and Pharmaceutical Engineering, NJIT
Dr. Wei Chen, Committee Member Date
Senior Research Investigator, Bristol-Myers Squibb Company, NJ
iv
BIOGRAPHICAL SKETCH Author: Priya Radhi Santhanam
Degree: Doctor of Philosophy
Date: September 2013
Undergraduate and Graduate Education:
Doctor of Philosophy in Chemical Engineering, New Jersey Institute of Technology, Newark, NJ, 2014
Master of Science in Chemical Engineering, New Jersey Institute of Technology, Newark, NJ, 2008
Bachelor of Technology in Chemical Engineering, Shanmugha Arts, Science, Technology and Research Academy (SASTRA), Thanjavur, T.N., India, 2007.
Major: Chemical Engineering Presentations and Publications: Santhanam, P. R. and E.L. Dreizin, Interaction parameters for Discrete Element
Modeling of powder flows. Submitted- Chemical Engineering Science. Santhanam, P.R., A. Ermoline and E. L. Dreizin, Discrete Element Model for an attritor
mill with impeller responding to interactions with milling balls. Chemical Engineering Science, 2013. 101: p.366-373.
Santhanam, P.R. and E. L. Dreizin, Real time indicators of material refinement in an
attritor mill. AIChE Journal, 2013. 59: p. 1088-1095. Santhanam, P.R. and E. L. Dreizin, Predicting conditions for scaled-up manufacturing of
materials prepared by ball milling . Powder Technology, 2012. 221: p. 404-411. Beloni, E., P. R. Santhanam and E. L. Dreizin, Electrical conductivity of metal powder
struck by a spark. Journal of Electrostatics, 2012. 70: p. 157-165.
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Santhanam, P.R., V. K. Hoffmann, M. A. Trunov and E. L. Dreizin, Characteristics of
aluminum combustion obtained from constant-volume explosion experiments.
Combustion Science and Technology, 2010. 182: p. 904-921.
Conference Proceedings:
Santhanam, P.R. and E. L. Dreizin, Characteristics of metal combustion obtained from
constant volume explosion experiments, 48th AIAA Aerospace Sciences Meeting
Including the New Horizons Forum and Aerospace Exposition, Article number
2010-0178, 2010.
Presentations:
Santhanam, P.R. and E. L. Dreizin, Responsive Discrete Element Model for preparation of
advanced materials by mechanical milling using an attritor mill. AIChE Annual
Meeting, Pittsburgh, PA, November 2012.
Santhanam, P.R. and E. L. Dreizin, Experimental indicators of progress in material
refinement by ball milling. TMS Annual Meeting, Orlando, FL, March 2012.
Santhanam, P.R. and E. L. Dreizin, Experimental indicators of progress in material
refinement by mechanical milling. Graduate Student Research Showcase, New
Jersey Institute of Technology, Newark, NJ, November 2011.
Santhanam, P.R. and E. L. Dreizin, Scale-up studies of aluminum matrix composites
prepared by ball milling. AIAA Region I Young Professional, Student, and
Education Conference, Baltimore, MD, November 2011.
Santhanam, P.R. and E. L. Dreizin, Experimental indicators of materials processing in
mechanical alloying and reactive milling. AIChE Annual Meeting, Minneapolis,
MN, October 2011.
Santhanam, P.R. and E. L. Dreizin, Predicting conditions for scaled-up manufacturing of
materials prepared by ball milling. Materials Processing and Manufacturing
Division, TMS Annual Meeting, San Diego, CA, February 2011.
Santhanam, P.R. and E. L. Dreizin, Experimental and computational study of progress in
material refinement by mechanical milling. Eastern Analytical Symposium and
Exposition, Somerset, New Jersey, November 2010.
Santhanam, P.R. and E. L. Dreizin, Predicting conditions for scaled-up manufacturing of
materials prepared by ball milling. AIChE Annual Meeting, Salt Lake City, UT,
November 2010.
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}
Santhanam, P.R. and E. L. Dreizin, Experimental and computational study of progress in
material refinement by mechanical milling. Graduate Student Research Showcase,
New Jersey Institute of Technology, Newark, NJ, November 2010.
Santhanam, P.R. and E. L. Dreizin, Discrete Element Method modeling of preparation of
reactive nanomaterials by mechanical milling. Gordon Research Conference on
Energetic Materials, Tilton, NH, June 2010.
Santhanam, P.R. and E. L. Dreizin, Characteristics of metal combustion obtained from
constant volume explosion experiments. 48th AIAA Aerospace Sciences Meeting,
Orlando, FL, January 2010.
Santhanam, P.R., C. Badiola, A. Ermoline, M. Schoenitz, and E. L. Dreizin, Discrete
Element Method modeling of preparation of reactive nanomaterials by mechanical
milling. AIChE Annual Meeting, Nashville, TN, November 2009.
Dreizin, E.L. and P. R. Santhanam, Characteristics of metal combustion obtained from
constant volume explosion experiments. 40th International Annual Conference of
ICT, Karlsruhe, Federal Republic of Germany, June 2009.
Santhanam, P.R. and E. L. Dreizin, Characteristics of metal combustion obtained from
constant volume explosion experiments. AIAA Region I-NE Student Conference,
Worcester, MA, March 2009.
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}
To my parents:
Santhanam Appa and Jeyanthi Amma-
THANK YOU. You believed in me even when I did not believe in myself.
Gurumurthy Appa and Bhanumathi Amma-
For your unconditional support.
To my husband, Ram-
We did it!
This kept me going:
“Worry never robs tomorrow of its sorrow, but only saps today of its strength.”
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ACKNOWLEDGMENT
My life as a graduate student has been a fulfilling experience-packed with beautiful
discoveries and wonderful opportunities! I have a lot of people to thank for making the
journey worthwhile.
Words cannot express the gratitude and admiration I feel for Dr. Dreizin. He has
played a pivotal role in my graduate life as my thesis advisor and a fantastic mentor for my
professional career. I thank him wholeheartedly for inspiring me and always providing a
positive outlook towards research. Thank you- for keeping the passion and love for
research alive in me, and all the students in our research group.
I would like to thank Dr. Schoenitz for always providing constructive criticism at
various meetings. His attention to detail is truly remarkable and helped greatly in
improving certain sections of this work. Many thanks are due to my committee members
Dr. Davé, Dr. Bilgili and Dr. Chen for agreeing to participate and for the insights. Their
experiences are in diverse research areas and I benefitted greatly from inputs from these
illustrious researchers.
I acknowledge Vern Hoffman for his help with building the vibratory hopper set-up.
Thanks to Dr. Alexandre Ermoline for assistance with debugging the C++ codes.
I would also like to recognize the current as well as graduated students in our lab;
Dr. Demetrios Stamatis, Dr. Ervin Beloni, Dr. Shasha Zhang, Yasmine Aly, Carlo Badiola,
Shashank Vummidi, Rayon Williams, Hongqi Nie, Ani Abraham, Amy Corcoran, Song
Wang and Stefano Mercati. Brainstorming, learning and working with everyone has been a
great pleasure and I will leave with fond memories of the time spent with them.
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A special thank you to Ms. Gonzalez and Dr. Ziavras from the Graduate Studies
office at NJIT for their valuable inputs in making this manuscript look better.
I discovered a great support system in the Society of Women Engineers (SWE)
chapter at NJIT. Many thanks to all the SWE ladies at NJIT and all over the nation. They
serve as great role models to all the female students in the engineering discipline.
I must acknowledge my family and friends for their unconditional support
throughout my student life. My parents, who sent me to America against all odds; so that I
could receive an education that they could only dream of. I know they had a vision for my
future and I hope I have fulfilled their ambitions. A big thank you to my parents-in law- for
welcoming me in their hearts and home, accustoming to my life as a graduate student and
for showering me with abundant love and support. Special thanks to my best friends and
the sisters I never had, especially Lakxmi Gurumurthy, Sangeetha Ramamurthy and
Supraja Varadharajan; for some great advice and ‘the talk’ whenever I needed it!
Lastly, and most importantly, I would like to thank my husband, Ram Gurumurthy.
He deserves immense gratitude and respect for his support and encouragement. I could not
have achieved everything I did during my graduate student life without his positive
attitude, encouragement and patience. They say that good work-life balance stems from
choosing the right life partner-I am glad we chose each other!
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TABLE OF CONTENTS
Chapter Page
1 INTRODUCTION……............................………………..…………………………. 1
1.1 Background …............................………………..……………………………... 1
1.2 Objectives …………….………………………………………………………... 4
2 PREDICTING CONDITIONS FOR SCALED-UP MANUFACTURING OF
MATERIALS PREPARED BY BALL MILLING………………………….………
6
2.1 Introduction ……………………………………………………………..……... 6
2.2 Experimental ……………………………………………….………………….. 9
2.2.1 Materials ……………………………...………………………………… 9
2.2.2 Milling Devices and Parameters…… ……...……………………………
2.2.3 Milling Progress Assessment: Yield Strength Measurement…………..
9
10
2.3 DEM Description ..………………………………………………………..……
12
2.3.1 Model Details…………………………………………..………………... 12
2.3.2 Experimental Evaluation of Friction Coefficients…..…… …………......
2.3.3 Descriptions of Different Milling Devices……………………………...
13
17
2.4 Results ……………………………………………………....………………….
2.4.1 Yield Strength as an Indicator of Milling Progress…………………….
2.4.2 Predicted Energy Dissipation Rate……………………………………..
2.5 Discussion………………………………………………………………………
2.6 Conclusions……………………………………………………………………
18
18
20
25
33
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TABLE OF CONTENTS
(Continued)
Chapter Page
3 REAL TIME INDICATORS OF MATERIAL REFINEMENT IN AN
ATTRITOR MILL…………………………………………..……………………....
35
3.1 Introduction ………………………………………………………………...….. 35
3.2 Experimental …………………………………………………………………...
3.2.1 Materials ……………………………...…………………………………
3.2.2 Milling Devices and Conditions……………………………………….
41
41
42
3.3 Milling Progress Indicators..………………………….…..………………….....
3.3.1 Material Characteristics………………………………...………………..
42
42
3.3.2 Real Time Milling Progress Indicators…………………………………..
3.4 Results………………………………………….…..…………………………...
44
45
3.4.1 Particle Shapes and Sizes....………………………………………….... 45
3.5
3.6
3.4.2 Yield Strength………………………………………………………….
3.4.3 X-ray Peak Width…………………………………………………………..
3.4.4 Real-Time Measurements……………………………………………….
Discussion………………………………………………………………………
Conclusions……………………………………………………………………..
50
51
52
55
58
4 DISCRETE ELEMENT MODEL FOR AN ATTRITOR MILL WITH IMPELLER
RESPONDING TO INTERACTION WITH MILLING BALLS…………………..
4.1 Introduction……………………………………………………………………..
4.2 Materials and Methods………………………………………………………….
4.2.1 Experimental……………………………………………………………..
4.2.2 Model…………………………………………………………………….
60
60
63
63
67
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TABLE OF CONTENTS
(Continued)
Chapter Page
4.3 Results …..………………………………………….….….…………………… 72
4.4 Discussion ……………………………………………………………………...
4.4.1 Predicting Power Dissipation…………………………………………..
4.4.2 Evaluation of the Milling Dose………………………………………...
4.5 Conclusions ……………………………………….…..……………………...
77
77
78
83
5 INTERACTION PARAMETERS FOR DISCRETE ELEMENT MODELING OF
POWDER FLOWS……….…………………………………………………………
5.1 Introduction……………………………………………………………………...
5.2 Experiments and Materials………………………………………………………
5.2.1 Experimental Setup……………………………………………………….
5.2.2 Vibration Characteristics………………………………………………….
5.2.3 Materials......................................................................................................
5.3 Model…………………………………………………………………………..
5.4 Results………………………………………………………………………….
5.4.1 Experimental Results……………………………………………………
5.4.2 Predicted Powder Flow Patterns………………………………………...
5.4.3 Sensitivity of DEM Predictions to Coefficients of Restitution and
Fricton…………………………………………………………………
5.4.3.1 Restitution Coefficient…………………………………………..
5.4.3.2 Friction Coefficient……………….…………………………….
5.4.3.3 Static vs. Rolling Friction……………………………………….
85
88
88
88
90
94
95
96
96
98
101
102
103
104
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TABLE OF CONTENTS
(Continued)
Chapter Page
5.4.4 Sensitivity of DEM Predictions to Particle Size Distribution……........ 106
5.4.5 Sensitivity of DEM Predictions to Vibration Amplitude………………. 107
5.4.6 Sensitivity of DEM Predictions to the Type of Vibratory Motion……… 108
5.5 Particle Interaction Parameters for Zirconia Beads............................................ 109
5.6 Discussion……………………………………………………………………... 112
5.7 Conclusion…………………………………………………………………….. 114
6 CONCLUSIONS AND FUTURE WORK………………………………………..... 116
6.1 Conclusions ………….……………………………………………………….. 116
6.2 Future Work……………………………………………………………….. …. 121
APPENDIX A REAL-TIME INDICATORS OF MILLING PROGRESS:
CRYOGENIC SYSTEMS…………………………………………… 125
APPENDIX B EFFECT OF HARD-SOFT COMPONENTS IN ATTRITOR MILL
PROCESSING……………………………………………………… 126
APPENDIX C DETAILED LIST OF ALL PERFORMED SIMULATIONS………... 128
APPENDIX D ALUMINUM TITANIUM SYSTEM STUDY FOR MILLING
PROGRESS………………………………………………………… 129
APPENDIX E FRICTION COEFFICIENT RESULTS……………………………… 130
APPENDIX F AMPLITUDE RESULT DETAILS………………………………… 131
APPENDIX G ADDITIONAL RESULTS FOR DIFFERENT MATERIAL
SYSTEMS (ADDENDUM TO CHAPTER 5)……………………… 132
APPENDIX H TRANSFER OF PARAMETERS FROM PLANETARY TO
ATTRITOR (IN-SITU MEASUREMENTS)………………………. 136
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TABLE OF CONTENTS
(Continued)
Chapter Page
APPENDIX I RESULTS FOR LARGER ATTRITOR VIALS…………………. 138
REFERENCES……………………………………………………………………… 142
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LIST OF TABLES
Table Page
2.1 Milling Conditions Used for Different Ball Mills………..……………………… 10
2.2 Data for Comparison of Predicted and Experimental Milling Progress and
Milling Times……………………………………………………………………
24
2.3 Corrected Data for Comparison of Predicted and Experimental Milling Progress 33
3.1 Material Properties of Pure Powders in Comparison to Milling Media…………. 41
4.1 Average Mass of Powder Coating Per Milling Ball for Different Mills…………….. 64
4.2 Friction Coefficients Characterizing Different Milling Configurations…………. 66
4.3 Comparison of Milling Dose and Associated Parameters for Three Milling
Devices……………………………………………………………………………
80
5.1
5.2
5.3
5.4
B.1
C.1
D.1
E.1
Rolling Friction Empirical Correlations …………………………..……………..
Vibration Amplitudes for Different Frequencies Obtained from the Image
Processing………………………………………………………………………...
Initial Values of Restitution and Friction Coefficients Used in EDEM………….
Qualitative Effect of Change in Interaction Parameters on the Discharge Rate at
Different Vibration Frequencies.............................................................................
List of Hardness Values for Materials....................................................................
Detailed List of all Performed Simulations in Chapter 5........................................
Milling Parameters for Aluminum Titanium System.............................................
Friction Coefficient Processing Results..................................................................
87
92
96
110
126
128
129
130
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LIST OF FIGURES
Figure Page
2.1 (Left) Loading curves from Instron device (Right) Fitting parameters using the
modified Heckel equation to obtain yield strength.……..……………………... 12
2.2 A video frame used for tracking the vertical position of the rolling ball. A
dashed circle shows the initial ball position. The planetary mill vial shown was
taken out after 30 minutes of milling……………………………………………..
14
2.3 Predicted changes of the vertical position of the rolling ball as a function of time
compared to the ball locations measured from the video. ‘S’ and ‘R’ in the
legend represent values of static and rolling friction coefficients, respectively….
15
2.4 DEM models of the three milling devices. The left image shows the shaker mill,
the center image is the planetary mill (350rpm) and on the right is the attritor
mill (400rpm)……………………………………………………………………..
17
2.5 Yield strength for different samples as a function of milling time. SM, PM and
AM represent shaker mill, planetary mill and attritor mill respectively………….
18
2.6 Backscattered electron images of milled aluminum-magnesium oxide composite
powders prepared at different milling times using planetary mill operated at 350
rpm………………………………………………………………………………..
19
2.7 Energy dissipation averaged per 1 ms as a function of time for different milling
conditions………………………………………………………………………....
21
2.8 Energy dissipation averaged per 1 ms as a function of time for different milling
conditions presented in the expanded time scale…………………………………
23
2.9 Histograms sorting interaction events of milling tools based on the average
force………………………………………………………………………………
26
2.10 Histograms sorting interaction events of milling tools based on the event
duration……………………………………………………………………….......
27
2.11 Fraction of energy dissipated in different mills as a function of average force
observed in individual events of milling tools interaction……………………….
30
2.12 Fraction of energy dissipated in different mills as a function of duration of
individual events of milling tools interaction…………………………………….
32
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LIST OF FIGURES
(Continued)
Figure Page
3.1 X-ray diffraction pattern for Al·B4C sample recovered from the attritor mill
after 2 hours; the FWHM is marked……………………………………………...
44
3.2 Real-time milling process parameters recorded for an Al·B4C sample after its
2-hour milling…………………………………………………………………….
45
3.3a Al·MgO SEM images of samples recovered after 1 hour of milling……………..
46
3.3b Al·B4C SEM images of samples recovered after 0.5 hour of milling……………
47
3.4a Al·MgO SEM images of samples recovered after 2 hours of milling………………..
47
3.4b
Al·B4C SEM images of samples recovered after 1 hour of milling………………… 48
3.5a Al·MgO SEM images of samples recovered after 4 hours of milling……………….. 48
3.5b Al·B4C SEM images of samples recovered after 4 hours of milling………………... 49
3.6 Yield strength for Al·MgO and Al·B4C samples recovered at different milling
times………………………………………………………………………………….
50
3.7 FWHM for aluminum XRD peak at 44.5º as a function of milling time…………….
51
3.8 Real-time milling process parameters recorded for an Al·B4C sample after its 2-
hour milling (cf. Fig. 2) shown with an expanded time scale………………………..
53
3.9 Average values and corresponding standard deviations for real-time indicators
measured to assess milling progress as a function of the milling time………………
54
3.10 Changes in power measured in real time during ball milling compared to changes in
parameters of the powder samples (yield strength and FWHM) recovered at
different milling times for Al·MgO and Al·B4C composites………………………...
56
4.1 Torque and rotation rate measured in experiments with different vial loads………...
67
4.2
Model description of the vial with impeller…………………………………………. 69
4.3 Schematic diagrams of impellers with different masses. A, B, C are respectively the
impellers with its actual mass, double, and triple mass………………………………
70
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LIST OF FIGURES
(Continued)
Figure Page
4.4 Relationship between torque and rotation speed of impeller as obtained from real-
time measurements…………………………………………………………………...
71
4.5 Calculated and experimental instantaneous values of rotation rate, torque, and
power. Impeller design A (cf. Figure 4.3) was used in calculations…………………
73
4.6 Results of parametric investigation: average power and its standard deviation at
different vial loads for model and experiment. The model results are shown for
three impeller designs A, B and C……………………………………………………
75
4.7 Horizontal coordinates of the bottom tip of the impeller for designs A, B, and C….. 76
4.8 Comparison of average and standard deviation in powder from EDEM and
experiments…………………………………………………………………………..
77
4.9 Histograms sorting interaction events of milling tools based on the average force
for different milling devices………………………………………………………….
79
4.10
5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
Milling dose predicted based on the entire powder load, Dm, and an alternatively
defined milling dose defined based on the mass of the powder coated onto the
milling balls…………………………………………………………………………..
Schematic of experimental set-up. In the inset, all dimensions are in mm……….
Typical PMT measurement……………………………………………………….
A photograph of a motionless exit tube (left) and a mirror image of the overlaid
images of the vibrating and motionless tube (right). The gray band shows the
displacement of the tube edge used to estimate the amplitudes for modeling
studies…………………………………………………………………………….
Sound waves recorded at different frequencies…………………………………..
Sample wave match for EDEM based on experimental measurement (120Hz)….
SEM image of Zirconia beads……………………………………………………
Size distribution of Zirconia beads (from SEM image processing)………………
Comparison of discharge rates estimated from the hopper mass change vs. that
inferred by the counted PMT peaks………………………………………………
82
89
90
91
92
93
94
95
97
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LIST OF FIGURES
(Continued)
Figure Page
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
Percentage of powder removed from the hopper in vibration runs using different
frequencies………………………………………………………………………..
Frames from EDEM illustrating motion patterns of particles inside the hopper
for different frequencies. The particle velocities are color-coded………………..
Velocity histograms for interaction events obtained from EDEM for the
simulations at different frequencies; data represent integration of results over
0.1s………………………………………………………………………………..
Effect of coefficient of restitution; vibration frequency 240 Hz (Runs 1-3, Table
C.1)……………………………………………………………………………….
Effect of coefficient of restitution: particle vs. wall interactions; vibration
frequency 240 Hz (Runs 3-5, Table C.1)…………………………………………
Effect of friction coefficient: particle vs. wall interactions; vibration frequency
240 Hz (Runs 2, 6-8, Table C.1).............................................................................
Effect of individual static and rolling friction coefficients for PP interactions;
vibration frequency 240 Hz. (Top: Runs 9-11; Bottom: Runs 12-14, Table C.1)..
Effect of individual static and rolling frictions for PW interactions; vibration
frequency 240 Hz. (Top: Runs 13, 15; Bottom: Runs 13, 16, Table
C.1)………...
Effect of using a size distribution on the discharge rate (Runs 2, 17-19, Table
C.1)…………………………………………………………………………….....
Sensitivity of different frequencies to change in amplitude. (Runs 1, 20, 21, in
Table C.1)...............................................................................................................
Effect of using a single size wave vs. a modulated wave on discharge rate.
(Runs 22- 27 in Table C.1).....................................................................................
Effect of change in individual parameters for different frequencies (Runs 25-30
in Table C.1). The legend shows the values of friction and restitution…………
Discharge rate for different frequencies conducted using a modulated wave.
Effect of using a higher number of particles is shown (Runs 28-33 in Table C.1)
98
99
101
102
103
104
105
106
107
108
109
111
112
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LIST OF FIGURES
(Continued)
Figure Page
A.1
B.1
B.2
D.1
F.1
G.1
G.2
G.3
G.4
G.5
H.1
I.1
I.2
I.3
I.4
I.5
Real-time measurements of impeller rotation speed, torque and power for five
systems. The average and standard deviations are shown......................................
Comparison of experimental milling time indicators for three material systems...
Comparison of real time milling progress indicators for three material systems...
Peak width data for Al-Ti prepared in different devices........................................
Amplitude data calculated at each frame for different frequencies........................
SEM Images of the three material systems.............................................................
Particle size distribution for the three cases............................................................
Discharge rate comparisons for various cases........................................................
Percentage mass exited at different frequencies for the three material systems....
Histograms of the measured voltage peaks for the three materials........................
Comparison of experimental and real-time milling progress indicators for
transfer of sample from planetary to attritor mill. (powder mass is 50g)………
Yield strength results for larger ceramic and steel vials relative to smaller
attritor vials………………………………………………………………………
DEM model of larger ceramic vial………………………………………………
Histograms of events sorted based on average force during the simulation for
smaller and larger vials are depicted……………………………………………...
Results of parametric investigation for ceramic 1400cc vial operated at 200rpm..
Power data from EDEM and data acquisition for different cases…………….......
125
126
127
129
131
132
133
134
134
135
136
138
139
139
140
141
1
CHAPTER 1
INTRODUCTION
1.1 Background
Mechanical milling is a technique widely used for powder processing. In the field of
energetic materials, high-energy milling is attractive for preparation of mechanically
alloyed, nano-composite, reactively milled, and mechano-chemically activated powders
[1-5]. In the past decade, ball milling has also expanded as a valuable tool in other
applications such as food [6, 7], pharmaceutical [8-10], energy storage [11, 12], military
and aircraft [13, 14], soil remediation [15] and even biomedical engineering [16]. Despite
the extensive uses, transition to practical manufacture in most cases is either extremely
slow or currently non-existent. The primary challenge is the lack of scientific
methodologies to transfer milling conditions form laboratory scale to large-scale
production. The problem is particularly daunting when milling devices are of different
scale or different operation type.
Before analyzing the development of scale-up models, an overview of existing
models to understand the ball milling process itself is presented. Historically, Benjamin
[17] pioneered applications of ball milling as a materials synthesis technique; his work
focused on dispersion strengthened alloys. In his earlier works, preliminary ideas for
rate-based models of mechanical alloying were presented. An expression for calculation
2
of average rate of change of lamellar thickness was established, which was indirectly
based on strain rate, and hardness of powders being milled. The core of that development
was based on the energy input to the powders being processed. Several authors, who
attempted to quantify and understand the ball milling process, adopted and further
developed this fundamental idea. The modeling studies can broadly be classified as
following atomistic [18-21] and mechanistic approaches [22-32].
As the name suggests, the atomistic models studied the mechanical alloying
process on an atomic scale using molecular dynamics approach [18-20] and
semi-empirical thermodynamic models [21, 33]. The repeated welding and fracture
mechanisms combined with temperature effects cause atomic level diffusion and result in
alloy phase formation. Deciphering such alloying mechanism was the goal of the
atomistic studies.
Mechanistic modeling involved use of mechanical properties of the powders and
balls to identify properties such as temperature rise during collisions, particle sizes,
hardness, etc. Originally, collisions were considered as the only means of energy transfer
[17, 22, 25] and appropriate kinematic equations were developed. Later, it was realized
based on theoretical understanding as well as video observations of ball mills that both
collisions as well as attrition (rolling or sliding) of the balls were essential contributors to
the energy transfer [28, 34] and more detailed models were developed.
3
Despite impressive analysis and results, the aforementioned attempts achieve
either empirical or semi-quantitative outcomes. Additionally, their usefulness for a
comprehensive understanding of the ball milling process or prediction of scale-up
parameters has not been demonstrated successfully. One of the breakthroughs in
development of quantitative parameter with potential use in scale-up studies came from
Delogu and Cocco [31, 32]. They introduced a simple milling dose parameter to relate the
energy transfer during the ball milling operation to the duration of milling. This concept
of milling dose was further developed by Jiang et al., [35] and Ward et al., [36] and its
applicability for descriptions of shaker and planetary mills was explored. This thesis will
advance that work and further establish milling dose as a useful concept for different
types of mills.
While the aforementioned authors investigated the fundamentals of the ball
milling processes, a few others ventured into understanding the mill operation via
numerical methods [37-42]. Specifically, Discrete Element Modeling (DEM) was
established to be an extremely valuable tool to model the ball milling devices [39-41].
Although the computational capabilities at the time of the early DEM efforts were not as
advanced as today, they certainly contributed to promote the understanding of the
process. Conventionally, one of the principal limitations in development of discrete
element models of ball mills has been identification of appropriate material properties as
well as interaction properties (restitution, friction coefficients). The material properties
4
can of course, be obtained easily from various literature sources. However, there are no
reports in literature of validated and suitable methods to estimate the correct values for
the interaction parameters. The discrete element modeling approach itself has been
around for a few decades, and a lack of studies for identification of the important
parameters for most DEM descriptions is quite striking.
1.2 Objectives
The general objective of this work includes development of a validated model describing
material refinement in different types of ball-milling devices, while accounting for
differences in the milling device type, scale and milling conditions. Milling dose will be
utilized to develop scale-up parameters. In the process of achieving the aforementioned
goal, a combination of experimental and modeling efforts will be presented in this thesis.
The modeling tool utilized in this work is commercially available EDEM software by
DEM Solutions.
The following specific objectives are proposed:
1. Create DEM-based models to describe various milling devices. Develop a scale-up
approach and validate outcomes from the mill models with appropriate
experiments. Meanwhile, obtain unique, powder dependent milling media
interaction parameters for use in the DEM models.
2. Identify a non-intrusive technique to obtain parameters that can aid in validating
the scale-up models. Specifically, examine the feasibility of using real-time
parameters measured during the actual milling experiment as milling progress
5
indicators to replace the labor-intensive, sample interrogation based experimental
methods employed currently.
3. Investigate the use of in-situ indicators of milling progress in tailoring the existing
DEM models. This will help to better reflect the actual operation of milling
devices, and thus, improve the efficacy of the scale-up models.
4. Develop a novel methodology to obtain material-dependent, particle-level
interaction parameters (friction and restitution coefficients) for DEM studies in
general.
6
CHAPTER 2
PREDICTING CONDITIONS FOR SCALED-UP MANUFACTURING OF
MATERIALS PREPARED BY BALL MILLING
2.1 Introduction
Mechanical milling is used to prepare a wide range of materials [4, 43]. Specific
examples include powders with reduced particle sizes [44], amorphous and
nano-structured alloys [45, 46], metal-organic composites [47], and reactive materials
such as mechanically alloyed or composite powders with components capable of highly
exothermic reactions [48, 49]. Laboratory scale synthesis enables a relatively tight
control over the structure, composition and morphology of the prepared materials. When
demand for newly developed materials increases, the laboratory processes need to be
transferred to practical manufacturing methods, which is an important challenge. The
scale-up difficulties are primarily due to the absence of validated models describing
material refinement in ball mills quantitatively. It is imperative to develop such models
capable of predicting milling progress for different milling devices without the need for
device- or material-specific adjustable parameters.
In a useful model, parameters describing material refinement should be obtained
as a function of the milling conditions. Material refinement is expressed through
evolution of specific material parameters of interest, such as the average particle size or
the fraction of the intermetallic phase formed as a result of milling. These material
7
parameters should be correlated with the process- and device-specific characteristics
describing energy transfer from milling tools to the milled materials. Such process
characteristics may be difficult to describe quantitatively, considering multiple types of
interactions between the milling tools, milling container, and the milled powder. Most
importantly, the relationships between the process characteristics and the rate of material
refinement have not been well understood and appear to vary as a function of the milling
conditions or for different milling devices. Earlier, it was suggested that milling progress
can be expressed using a function called milling dose, Dm [31, 36] defined as the ratio of
the energy transferred to the powder from the milling tools, W to the mass of the milled
powder, mp:
/m pD W m (2.1)
Ward et al. and Jiang et al. [35, 36] used milling dose to track preparation of reactive
nanocomposite powders, for which the refinement of components (size of oxide
inclusions in a metal matrix) served as the material specific parameter of interest.
Assuming steady milling conditions, the energy transferred to the powder was expressed
as a product of the rate of energy dissipation in the ball mill, Ed, and the milling time, t.
Thus, milling dose was expressed as a function of milling time:
8
/m d pD E t m (2.2)
Thus, if the milling time required to prepare a specific product is determined
experimentally, milling dose specific for that product is directly proportional to the
energy dissipation rate. Multiple recently developed Discrete Element Models (DEM)
describing the motion of the milling tools [38, 50] enable a relatively straightforward
calculation of the energy dissipation rate. However, DEM describes the motion of the
milling tools and not the milled powder. Therefore, two main challenges in utilizing the
DEM predictions are:
Account for the effects of the milled material on the motion of and energy exchange
between the milling tools;
Determine which fraction of the energy dissipated in interactions between the
milling tools is responsible for the refinement of the milled material (parts of the
energy can be used to heat the entire milling container, deform or damage the
milling tools, or simply move the milled material without refining it.)
Previously, the presence of milled material on the motion of the milling tools was
accounted by appropriate selection of the restitution coefficient describing collisions of
the milling balls coated with powder [36, 51]. However, the effect of the milled material
on the friction coefficients was not addressed. Furthermore, rolling friction was not
explicitly considered in some of the previously reported DEM calculations, and it was
9
shown that such an omission results in a gross underestimation of the energy dissipated in
a planetary mill and used to refine the milled powders [36].
This effort is aimed to develop a DEM-based model and approach for interpreting
the computational results enabling an adequate description of the milling progress. The
approach should be suitable for applications involving both manufacturing and
processing of materials using different ball-milling devices.
2.2 Experimental
2.2.1 Materials
The materials for milling experiments were selected to enable measurements of the yield
strength of the prepared composite increasing as a function of the milling progress.
Powders of pure aluminum (-325 mesh, 99.9% pure, by Atlantic Equipment Engineers)
and magnesium oxide (-325 mesh, 99% pure, by Aldrich Chemical Company, Inc.) were
blended together for green mixture. These components do not react chemically, so the
product of the ball milling is a work-hardened composite material. The starting powder
blend included 30% aluminum and 70% magnesium oxide by volume.
2.2.2 Milling Devices and Parameters
Prepared powder blends were ball milled using three devices: a SPEX 8000 shaker mill, a
Retsch 400 PM planetary mill, and a Union Process HD 01 attritor mill. The process
10
control agent was stearic acid (1% by wt.). Steel balls with 9.5 mm nominal diameter
were used in all three mills. The milling jar of the attritor mill was cooled with room
temperature water. Milling jars of the shaker mill were cooled using room temperature
compressed air flow. Finally, the temperature in the milling compartment of the planetary
mill was kept at 15 ºC using an air conditioner attached to the mill. Milling times varied
from 30 min to 8 hours. Other milling conditions are shown in Table 2.1.
Table 2.1 Milling Conditions Used for Different Ball Mills
Parameter Shaker
mill
Planetary
mill
Attritor
mill
Charge Ratio (ball to powder mass ratio) 10 3 36
Powder mass, g 5 30 50
Rotation speed, rpm 1054
(fixed) 300, 350 200, 400
Impeller dimensions
(vertical shaft, four
horizontal bars), mm
Length N/A N/A 86.2
Diameter N/A N/A 25.2
Bar length N/A N/A 51.9
Bar diameter N/A N/A 10.4
Vial dimensions, mm Height 52.4 51.4 101.6
Diameter 26.4 101.6 76.2
2.2.3 Milling Progress Assessment: Yield Strength Measurement
Different material parameters have been used to assess the milling progress in the past,
ranging from particle size [4], grain size refinement [4, 52], to the ignition temperature of
the ball-milled powder [53, 54]. In this study, preliminary experiments considered
changes in the particle size for brittle materials and development of intermetallic phases
11
for mechanically alloyed powders. It was observed that the particle size changes very
rapidly for brittle powders, such as sand, so that it is difficult to identify the rate of its
change during milling with steady conditions. Changes in particle morphology (such as
flake formation) masked the changes in the particle sizes for ductile powders. It was also
observed that multiple intermediate and difficult to quantify phases are formed in
mechanically alloyed powders making formation of such phases an inconvenient
indicator of the milling progress. Following these preliminary studies, a change in the
yield strength of the work-hardened oxide-reinforced composite powders was selected as
an experimental indicator of the milling progress.
The compression curves (Figure 2.1, Left) were measured while consolidating
prepared powders into pellets using an Instron 5567 universal strength tester. At least
three pellets were made out of each sample obtained from the milling experiment. The
cross-head extension rate used for the test was 0.6 mm/min and the maximum load
applied was 30,000N.
The yield strength, σ0 was found from experiments on compaction of the prepared
powders by fitting the measured compression curves for porosity, e, as a function of
pressure, P (Figure 2.1, Right), using a modified Heckel equation [55]:,
1
0 1 0
1 1 1ln ln ln 1
3
k P
e e k
(2.3)
12
where e0 is the initial porosity of the compact and k1 is a parameter based on Poisson’s
ratio. Both initial and current porosity values were calculated using theoretical maximum
density of the material and the volume of the powder being consolidated.
P
0 50 100 150 200 250ln
(1/e
)
-4.5
-4.0
-3.5
-3.0
-2.5
-2.0
-1.5
Compressive extension, mm
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5
Com
pre
ssiv
e loa
d, N
0
5000
10000
15000
20000
25000
30000
Figure 2.1 (Left) Loading curves from Instron device (Right) Fitting parameters using
the modified Heckel equation to obtain yield strength.
2.3. DEM Description
2.3.1 Model Details
Commercial EDEM software by DEM Solutions Inc. [56] was used to describe all the
milling devices. The Hertz –Mindlin (no slip) [57] contact model was used for the force
calculations. This is a soft-particle contact model [58] and it describes the behavior of
milling tools when they come into contact with one another. The time step for the
calculations was 1 µs.
The normal (Fn) and tangential (Ft) forces in the model are evaluated using
equations (2.4) and (2.5).
13
3
* * 24
3n nF Y R (2.4)
t t tF S (2.5)
where Y* is the equivalent Young’s Modulus, R
* is the equivalent radius, St is the
tangential stiffness and δn and δt are the normal and tangential overlaps respectively.
Unlike previous models [35, 36], the friction and restitution coefficients were accounted
for individually in this code. Coulomb friction limits the tangential force and is given by
µsFn, where µs is the coefficient of static friction. Also, the rolling friction µr is
incorporated by applying a torque (τi) to the contacting surfaces (Equation 2.6).
i r n i iF R (2.6)
where Ri is the distance of the contact point from the center of mass and ωi is the unit
angular velocity of the object at the contact point. The value of the restitution coefficient
was selected based on previous reports [36]. The values of the friction coefficients were
determined following the procedure outlined below.
2.3.2 Experimental Evaluation of Friction Coefficients
A dedicated experiment and respective DEM model were designed in order to obtain the
friction coefficients. In the experiment, a single ball was freely rolling within a milling
14
vial, as shown in Figure 2.2. Both ball and vial surfaces were coated by the milled
powder. The ball’s motion in this specific configuration was also described using the
DEM model. The values of rolling and static friction coefficients were selected to match
the predictions with the experiment.
To prepare the vial and the ball surfaces, Al and MgO mixtures were milled for
different times in the planetary mill. The powder and balls were removed from the vial
without disturbing the powder adhered to the vial surface; the vial was then placed
horizontally, as shown in Figure 2.2.
Figure 2.2 A video frame used for tracking the vertical position of the rolling ball. A
dashed circle shows the initial ball position. The planetary mill vial shown was taken out
after 30 minutes of milling.
A single ball from the milling experiment was dragged to the left-center position
(dotted circle in Figure 2.2) of the vial and then released. The ball motion included
15
several oscillations before it stopped at the bottom of the vial. The experiment was
videotaped using a camcorder. From the video, the heights and moments when the
topmost positions of the ball occurred were recorded. At those moments, the ball stopped
instantaneously, so that its image was less blurred in the videos. Open symbols in
Figure 2.2 show coordinates of the topmost positions of the ball as a function of time.
In parallel to experiments, a model of a single ball rolling down a planetary mill
vial wall was set up in DEM. The initial position of the ball in the DEM was set to be
identical to that in the rolling experiment. The output data extracted from this calculation
was the ball position as a function of time.
Time, s
0.0 0.5 1.0 1.5 2.0
Po
sitio
n Y
, m
m
0
5
10
15
20
25
30
35
40
Experiment
Model
S 0.3, R 0.05
S 0.3; R 0.01
S 0.1; R 0.05
Figure 2.3 Predicted changes of the vertical position of the rolling ball as a function of
time compared to the ball locations measured from the video. ‘S’ and ‘R’ in the legend
represent values of static and rolling friction coefficients, respectively.
16
The best match between the experimental and predicted ball trajectories was
found by systematically varying the values of static and rolling friction coefficients. It
was observed that the static friction affected the ball position at early times, when its
velocity was high, while rolling friction controlled the ball motion later, when it was
decelerating. Therefore, matching the experimental and measured ball’s trajectories
during the entire experiment enabled us to select the values for both coefficients.
Examples of the calculated ball trajectories, presented through the vertical coordinate as a
function of time are illustrated in Figure 2.3 for different values of the friction
coefficients.
Comparison of experimental and computational results, suggested that the rolling
and static friction coefficients should be taken as 0.05 and 0.3, respectively. For this
comparison, experimental data were collected using the milling vial and ball coated with
the powder formed as a result of 0.5 hour milling at 350 rpm (powder load 30 g). Note
that experiments were also performed with powders prepared as a result of milling for 1,
2 and 3 hours. Friction coefficients did not substantially change as a function of the
milling time. The static friction coefficient varied in the range of ± 30% from the above
values and the rolling friction coefficient remained consistent with that found for the
sample milled for 0.5 hours. A small change in the static friction was observed only for
the longest duration experiment (3 hours). It was further tested that the rates of energy
dissipation calculated by DEM were hardly affected by such small variations in the
17
friction coefficients. Therefore, all further calculations assumed constant friction
coefficients.
2.3.3 Descriptions of Different Milling Devices
Figure 2.4 presents the DEM models for the shaker, planetary and attritor mills. The ball
color represents its total energy and the color scale is the same for all the cases, red
indicating the highest energy and blue the lowest.
In the shaker mill, the balls are flying across the vial with the primary energy
dissipation coming from head-on collisions, consistent with the earlier report [36]. For
the planetary mill, the balls are rolling along the vial surface forming a relatively stable
two-dimensional structure, also similar to earlier results [35]. For the attritor mill, the
balls move much slower; at higher rpm some of the balls are observed to be airborne for
short periods of time.
Figure 2.4 DEM models of the three milling devices. The left image shows the shaker
mill, the center image is the attritor mill (400rpm) and on the right is the planetary mill
(350rpm).
18
2.4 Results
2.4.1 Yield Strength as an Indicator of Milling Progress
The yield strengths for samples prepared in the three milling devices as a function of
milling time are shown in Figure 2.5.
0 1 2 3 4 8
Milling time, hrs
40
50
60
70
80
90
100
110
120
Yie
ld s
tre
ng
th,
MP
a
Shaker
PM: 350 rpm
PM: 300 rpm
AM: 400 rpm
AM: 200rpm
/ /
Figure 2.5 Yield strength for different samples as a function of milling time. SM, PM
and AM represent shaker mill, planetary mill and attritor mill respectively.
The error bars show standard deviation of the values obtained by processing the
experimental loading curves for individual pellets. The yield strength initially seems to be
unaffected or even reduced for some of the experiments; however, for all mills and
milling conditions the yields strength is observed to increase at longer milling times.
Eventually, the value of the yield strength is stabilized. The initially stable or even
19
reduced yield strength is correlating with the formation of flakes, as illustrated in
Figure 2.6. Flakes were observed to form at short milling times in all ball mills. An
increase in the measured yield strength at longer milling times correlated with breaking
down the flakes and formation of composite equiaxial particles, as also shown in
Figure 2.6. When milling times increased further, the particle sizes decreased only
slightly, possibly explaining slight reduction in the yield strength of the materials.
Figure 2.6 Backscattered electron images of milled aluminum-magnesium oxide
composite powders prepared at different milling times using planetary mill operated at
350 rpm.
An increase in the yield strength above an arbitrarily selected value of 80 MPa,
shown as a dashed line in Figure 2.5 occurred reproducibly for all cases following
breaking down the flake-like particles. Yield strength just above this value was measured
for the samples recovered after about 30 min milling from the shaker mill, after about 1
and 2 hours for the planetary mill operated 350 and 300 rpm, respectively, and after about
2 and 4 hours for the attritor mill operated at 400 and 200 rpm, respectively. No
2 hrs
100 µm
30 min
100 µm
4 hrs
100 µm
20
significant difference in the particle sizes and shapes for the powders produced in
different mills at the above mentioned milling times could be detected. It was assumed
that the materials prepared by different mills are nearly identical. Therefore, it was
possible to select achieving the yield strength of 80 MPa as an indicator of the material
refinement. Milling times corresponding to the yield strength of 80 MPa achieved for
different milling devices and conditions were obtained as times at which the experimental
trends crossed the 80 MPa level, as shown in Figure 2.5. As discussed below, these times
together with the respective energy dissipation rates, Ed, computed by DEM and masses
of powder loaded in the vials, mp, were used to estimate the milling dose, Dm, for each of
the milling devices using equation (2.2). If the milling progress indicator is properly
selected, and if the energy dissipation rates calculated by DEM are proportional to the
milling progress, the value of Dm should be the same for all powders, indicating the same
level of refinement achieved by ball milling.
2.4.2 Predicted Energy Dissipation Rate
It is interesting to begin analysis of the DEM calculation by comparing the average
energy dissipation rates for different milling devices. Results in terms of energy
dissipated in the entire milling vial averaged per 1 ms are shown in Figure 2.7.
21
Attritor400rpm
Attritor200rpm
Planetary300rpm
0.00010.001
0.010.1
110
0.00010.001
0.010.1
1
Shaker
Planetary350rpm
0.00010.001
0.010.1
1
Ene
rgy d
issip
ation
rate
, kW
0.000010.0001
0.0010.01
0.11
Simulation time, s
0 2 4 6 8 100.00001
0.00010.001
0.010.1
1
Figure 2.7 Energy dissipation averaged per 1 ms as a function of time for different
milling conditions.
Fractions of the same traces are shown in the expanded time scale in Figure 2.8. A
relatively short time interval over which the energy dissipation is averaged is selected to
observe device-specific trends associated with particular ball motion patterns.
The energy dissipated in the shaker mill varies between very low and moderate
values. Figure 2.8 suggests that the variations track the shaking motion of the vial and
respective motion of balls flying in the vial side to side. The balls in flight effectively do
not transfer any energy to the powder. When they strike the vial sides, the energy transfer
22
rates are substantially increased. For the planetary mill, the energy dissipation rates are
remarkably steady. This is understood considering that the balls are continuously rolling
along the vial surface. For the attritor mill, the energy dissipation rate is changing in a
broad range. The lower bound for the energy dissipation rate is higher for the 400 rpm
case as compared to 200 rpm case, as expected. However, multiple spikes with higher
energy dissipation rate appear in both traces and might even be stronger for the 200 rpm
case. Such spikes are formed when individual balls occasionally get jammed between
other balls and impeller and then released after being significantly compressed. Thus, the
energy predicted to be dissipated in such events may not be expended to refine the milled
powder; instead it is likely to be transferred directly to the balls causing their heating and
plastic deformation. Note that extended plastic deformation is not accounted for in the
current DEM model assuming only a limited plasticity for the milling balls. It is also of
interest to mention that events similar to the high-energy dissipation events observed here
were also reported in Rydin et al. [59]. Nevertheless, unlike the present effort, Rydin et
al. [59] referred to these events as “direct impacts” and were postulated to be more
effective for powder refinement than lower energy rolling and sliding events.
23
Attritor400rpm
Attritor200rpm
Planetary300rpm
0.00010.001
0.010.1
110
Figure 7_Energy_Raw_ed-close
0.00010.001
0.010.1
1
Shaker
Planetary350rpm
0.00010.001
0.010.1
1
En
erg
y d
issip
ation
rate
, kW
0.000010.0001
0.0010.01
0.11
Simulation time, s
6.00 6.02 6.04 6.06 6.08 6.100.00001
0.00010.001
0.010.1
1
Figure 2.8 Energy dissipation averaged per 1 ms as a function of time for different
milling conditions presented in the expanded time scale.
Using the calculated energy dissipation rates for all mills and milling conditions,
it is possible to compare the predicted milling progress with that observed
experimentally. Such a comparison is presented in Table 2.2.
24
Table 2.2 Data for Comparison of Predicted and Experimental Milling Progress and
Milling Times
Parameters
Milling Device
Attritor Planetary Shaker
200 rpm 400 rpm 300 rpm 350 rpm 1054 rpm
Ed/mp, kW/g 8.3±1.5 10.0±1.0 1.3±0.004 1.9±0.05 4.8±0.2
Experimental milling
time texp, to reach 80
Mpa yield strength, hrs
4.0±0.3 1.8±0.1 1.7±0.8 1.0±0.3 0.4±0.1
Milling dose,
expd
mp
E tD
m , kW·hr/g
33.3±8.0 18.0±2.8 2.1±1.0 1.9±0.6 1.9±0.5
Milling time, predicted,
tpred, hrs 0.23±0.08 0.19±0.06 1.5±0.46 1
* 0.4±0.13
*Selected as the reference experiment for choosing the appropriate milling dose
The energy dissipation rates (shown normalized per sample mass, as Ed/mp) were
calculated as averages for five time intervals, 0.1 s each. The ranges shown in Table 2.2
represent standard deviations for the obtained average values. They represent the
statistical variation in the DEM-calculated rates of energy dissipation. The ranges shown
for the experimental milling time, texp, reflect the error bars shown in Figure 2.5. The
values of milling dose calculated using equation (2.2) and experimental milling times are
shown to illustrate the practical use of the DEM results. If one of the milling conditions is
selected as a reference, prediction of the milling times required for all other conditions
should be possible using the reference milling dose. For example, the experimental
milling time of 1 hour observed for the planetary mill operated at 350 rpm is selected as
25
the reference. Using respective value of the milling dose of 1.9 kW·hr/g, milling times
are obtained using equation (2.2) and are shown in Table 2.2.
Based on the milling dose concept, all milling dose values in Table 2.2 are
expected to be identical to one another, considering that for all experiments, the
experimental milling time is taken as that required to achieve 80 MPa in yield strength
for all prepared materials. Indeed, within the expected error, the milling dose values are
identical to one another for the shaker mill and for both rpm values used for the planetary
mill. However, the predicted milling dose values for both rpm’s used for the attritor mill
are substantially greater than anticipated. Therefore, using the planetary mill operated at
350 rpm as a reference milling condition would result in significant under-predictions of
the milling times required for obtaining the same material in the attritor mill. The reasons
for this discrepancy and an approach to correct for it are discussed below.
2.5. Discussion
In order to understand the reasons for the apparent discrepancy between predictions and
experimental data, especially substantial for the attritor mill, it is useful to closely
examine how the energy dissipation from the milling tools occurs for each milling
condition. Energy is dissipated in discrete events or collisions. Each event is identified
when milling balls touch each other or touch the milling vial. As a first step, the energy
dissipation events for each milling condition were sorted based on the average force
26
exerted between interacting elements and based on the event duration. The results of the
above two classifications are shown in Figures 2.9 and 2.10, respectively. The event
statistics shown in Figures 2.9 and 2.10 represent results of DEM calculations for 10 s of
milling.
100
101
102
103
104
105
Shaker
100
101
102
103
104 Planetary:
350 rpm
Average force, N
10-4
10-3
10-2
10-1
100
101
102
103
104
105
Inte
ractio
n e
ve
nts
(co
llisio
ns)
100
101
102
103
104
100
101
102
103
104 Attritor:
400 rpm
100
101
102
103
104 Planetary:
300 rpm
Attritor: 200 rpm
Filtered out
Figure 2.9 Histograms sorting interaction events of milling tools based on the average
force.
27
100
101
102
103
104
105
Shaker
101
102
103
104
100
Planetary:350rpm
Collision duration, s
10-5
10-4
10-3
10-2
10-1
Inte
raction
eve
nts
(co
llisio
ns)
100
101
102
103
104 Attritor:
200rpm
100
101
102
103
104 Attritor:
400rpm
100
101
102
103
104 Planetary:
300rpm
Filtered out
Figure 2.10 Histograms sorting interaction events of milling tools based on the event
duration.
Histograms representing the number of interaction events sorted based on the
average force shown in Figure 2.9 are very similar to those obtained by sorting the
interaction events based on the maximum force (not shown for brevity). The range of
forces predicted to develop in the milling tool interactions for the planetary mill is
relatively narrow. This is readily understood considering that the ball motion pattern in
this case is most regular, compared to other milling devices. Somewhat greater forces are
observed for the shaker mill. This is also expected considering that such greater forces
28
result from multiple head-on collisions occurring in that device. The histograms observed
for the attritor mill exhibit multiple events characterized by very low forces. This is likely
associated with collective ball motion. The high-force end of the histograms for the
attritor appears to be irregular. It is apparent that the main distribution ends for events in
which forces are between 100 and 1000 N, similar to the high-force distribution edges for
the other milling devices. However, a high-force “tail” is also observed indicating a
relatively large number of events with very large forces. A close examination of such
individual interaction events shows that these are the same events causing spikes in the
energy dissipation traces (Figures 2.7 and 2.8) or “direct impacts” according to Rydin et
al. [59]. These events occur when an individual ball gets caught among other balls and is
severely compressed as the impeller continues pressing the balls together. As discussed
above, such events may indeed occur in experiment; however, the energy dissipated in
compression and release of such balls is unlikely to be transferred to the milled powder.
Therefore, it is of interest to filter out such events from the overall energy dissipation
analysis. The region proposed to be filtered out is shown in gray in Figure 2.9.
A similar examination of histograms showing interaction events sorted by the
event duration (Figure 2.10) suggests that some irregularity exists for the shaker mill, for
which the histogram appears to be by-modal. It is interesting that for all histograms, the
main peak occurs for durations under 0.1 ms, with the peak position shifting to longer
durations from the shaker mill to planetary and then to attritor mill. The distribution is
29
relatively narrow for the planetary mill. The right-side edge of the planetary mill
histogram effectively coincides with the right side edge of the first histogram peak
observed for the shaker mill. It is observed that longer interaction events for the shaker
mill occur when the balls roll along the vial surface. As was shown by Ward et al. [36],
only a very small energy is dissipated in such events, and this fraction of the energy
dissipation does not correlate with the material refinement observed experimentally.
According to recommendations of Ward et al. [36], such interaction events can also be
filtered out from the analysis of the energy dissipation. However, unlike the high force
interaction events filtered out for the attritor mill, removing of the low-energy collisions
for the shaker mill is not expected to appreciably change the total energy dissipation.
The effects of different types of interaction events on the energy dissipation rates
predicted by DEM can be seen clearly considering cumulative distributions of the energy
dissipation rates as a function of the force and collision duration. These cumulative
distributions are shown in Figures 2.11 and 2.12, respectively.
As shown in Figure 2.11, for the planetary mill most of the energy is dissipated in
relatively weak collisions. For the shaker mill, the energy is dissipated in collisions with
greater force. Filtering out longer collisions hardly changes the cumulative distribution
curve for the shaker mill. For the attritor mill, the distributions are somewhat peculiar.
The fraction of dissipated energy increases, as for the planetary mill, while the interaction
force increases to about 100 N. No head-on collisions produced by airborne balls (as in
30
the shaker mill) occur, so the fraction of the dissipated energy does not increase
appreciably as the force increases further. However, for very large forces, exceeding
approximately 1000 N, the energy dissipation rates predicted by DEM increase
dramatically. Clearly, removing such interaction events from analysis would drastically
reduce the energy dissipation rate and respective value of the milling dose, resulting in
reducing the discrepancy observed in Table 2.2.
Force, N
100
101
102
103
104
Fra
ctio
n o
f en
erg
y d
issip
ate
d
0.0
0.2
0.4
0.6
0.8
1.0
SM
PM: 350 rpm
PM: 300 rpm
AM: 400 rpm
AM: 200rpm
SM: Filtered
Figure 2.11 Fraction of energy dissipated in different mills as a function of average force
observed in individual events of milling tools interaction.
31
In addition to be characterized by the very high forces, the collisions that need to
be filtered out are very long. Indeed, the time required to compress the ball that is
jammed among other balls is relatively long, much longer than a typical interaction
resulting in refinement of the powder present on the surfaces of the colliding balls, vial or
impeller. Indeed, examining the cumulative distributions shown in Figure 2.12, it can be
noticed that for all devices, the fraction of the dissipated energy increases continuously as
the interaction events increase to about 1 ms. For both shaker and planetary mills, longer
interactions are unimportant. However, for the attritor mill, fraction of the dissipated
energy increases dramatically for much longer interaction events. Importantly, when the
events characterized by the abnormally high forces are filtered out (as suggested in
Figure 2.9), it is observed that the longer interaction events disappear as well.
32
Collision duration, s
10-6
10-5
10-4
10-3
10-2
10-1
Fra
ctio
n o
f e
ne
rgy d
issip
ate
d
0.0
0.2
0.4
0.6
0.8
1.0
SM
PM: 350 rpm
PM: 300 rpm
AM: 400 rpm
AM: 200rpm
AM: 400 rpm; Filtered
AM: 200rpm, Filtered
Figure 2.12 Fraction of energy dissipated in different mills as a function of duration of
individual events of milling tools interaction.
The milling dose can now be recalculated considering the DEM results corrected
by removing the interaction events with abnormally high forces occurring for the attritor
mill. For completeness, one can also consider the effect of correction resulting from
removal of longer collisions (second peak in the histogram shown in Figure 2.10) for the
shaker mill. The corrected results are shown in Table 2.3. For completeness, experimental
milling times shown in Table 2.2 and used to calculate the corrected milling dose are
repeated in Table 2.3. The discrepancy between different milling devices is substantially
reduced.
33
Table 2.3 Corrected Data for Comparison of Predicted and Experimental Milling
Progress
Parameters
Milling device
Attritor Planetary Shaker
200 rpm 400 rpm 300 rpm 350 rpm 1054 rpm
Corrected E*d/mp,
kW/g 0.4±0.002 1.7±0.06 1.3±0.01 2.0±0.04 4.6±0.1
Experimental milling
time texp, to reach 80
MPa yield strength,
hrs
4.0±0.3 1.8±0.1 1.7±0.8 1.0±0.3 0.4±0.1
Corrected milling
dose,
*exp* d
mp
E tD
m ,
kW·hr/g
1.6±0.1 3.06±0.3 2.1±1.0 2.0±0.6 1.8±0.5
Milling time,
predicted, tpred, hrs 5.6±1.8 1.2±0.4 1.6±0.5 1 0.4±0.14
2.6. Conclusions
In order to obtain a useful DEM description of the milling process, experimentally
validated values for restitution and friction coefficients are necessary. Both static and
rolling friction coefficients were obtained comparing simple experiments with
powder-coated milling balls rolling inside the milling vial versus respective DEM model.
Milling dose defined as the ratio of the energy transferred to the powder from the milling
tools to the mass of the milled powder provides a useful description of the milling
progress for different devices and milling conditions. The DEM-calculated rate of energy
dissipation multiplied by the experimental milling time enables one to calculate the
34
energy transferred to the powder from the milling tools. This energy determines the
material refinement. Once it is found for a material prepared in a specific milling
configuration, it can be used for predicting milling time required to prepare that material
using a new milling device or altered milling conditions. No corrections or adjustments to
the DEM calculations are necessary for both planetary and shaker mills. For attritor mill,
the rate of energy dissipation predicted by DEM includes substantial contribution from
the milling tool interaction events accompanied by abnormally high forces (>103 N) and
continuing for times exceeding 1 ms. Such events are associated with jamming milling
balls and their subsequent release at relatively high velocities. Because of very high
forces developed in such events, the energy is likely dissipated to heat or plastically
deform the milling tools rather than refine the milled material. Therefore, it is proposed to
filter out such high-force, long duration events from further analysis of powder
refinement in the attritor mill. Such filtering enables one to obtain a much better
correlation of the experimentally achieved powder refinement with DEM prediction.
Milling dose implied by the filtered DEM calculations for attritor mill becomes
comparable to that obtained for both shaker and planetary mills when all three milling
devices are used to achieve the same degree of material refinement.
35
CHAPTER 3
REAL TIME INDICATORS OF MATERIAL REFINEMENT IN AN ATTRITOR
MILL
3.1 Introduction
Mechanical milling is widely used for the preparation of various advanced materials [4].
Material is refined and modified as a result of multiple interactions with milling balls
occurring at different impact energies and configurations. Most commonly, the milling
progress is assessed by recovery of partially milled samples at regular time intervals.
Such samples are evaluated based on their particle sizes, shapes, crystal structures, or
mechanical properties to establish the time necessary to prepare the required material [52,
53, 60]. This approach is labor-intensive, and more streamlined methods capable of
quantifying the milling progress are desired.
In the past, several research groups have realized the difficulty in such tedious
experimental methodologies and tried to identify simpler approaches. Some of the
parameters investigated to aid in understanding milling process include measurement of
power consumption and torque from the motor attached to the mill [61-64], measurement
of temperature inside the milling vial [35, 36, 62], measurement of vibration frequency,
amplitude of the vial and impact frequency of ball [65], and visualization by recording
high speed videos of the milling process [59].
36
One of the early attempts at such real-time diagnostics was by R Goodson et
al. [61], who utilized Charles equation correlating the specific energy input to the mill E
(in kW.hr/ton or W. hr/Kg), and median particle size dp (in micron), (E=Adpα), where A
and α are parametric constants. The milling experiment was carried out using a laboratory
attritor and the sample was a mixture of tungsten carbide and cobalt (6 wt% and 12 wt%)
powders. Three different milling conditions were monitored: control run at 125 rpm, run
with 25% less balls and high speed run at 200 rpm. The specific energy input data for the
Charles equation was obtained from the power draw for the mill. The idea was to be able
to postulate the appropriate milling parameters for the final products of the desired size
range. The energy input as a function of different filling of the vial volume was also
measured. After milling, the powder samples were pressed and vacuum sintered. The
density, coercivity, Rockwell hardness and specific magnetic saturation of milled and
sintered cylinders were measured as functions of milling time. As an initial attempt, the
established correlation between the specific energy input and median particle sizes seems
reasonable. However, the theory has not been extended to other materials of interest.
Also, it is concluded that the desired final product size can be predicted solely based on
the Charles equations and hence, the energy input to the mill alone. In other words, an
independence of the final product on milling conditions is claimed, but this major
comment has not been not thoroughly validated.
37
Kimura and Takada [62] set up a data acquisition system on a custom rotating
arm ball mill (similar in operation to the attritor mill used in this work). Apart from the
torque on the rotating arm, the temperature inside the vial was also monitored as a
function of milling time. The aim was to track a solid-state amorphization transformation
in Co-Zn alloys. The measured torque was established to be sensitive to changes in
powder structure, whereas the attrition temperature was proposed to be a direct indicator
of the kinetics of solid-state amorphizing transformations. Overall, the only major
outcome is that when there is a reduction in the torque and a spike in the temperature, this
would indicate that an exothermic solid-state reaction has occurred in the powders. Apart
from this result, which is specific to the material system under consideration, no
diagnostic methodology with universal appeal was developed. Besides, the same theory
was not extended to other systems with similar amorphization reactions as a further proof
of concept. Although the data acquisition seems to be reasonably sensitive to changes in
the mill, the milling device itself is not commercial available for use.
Temperature measurement was also considered as a reaction progress monitor in
some of the earlier projects from the present research group [35, 36]. The systems under
consideration included mechanically alloyed Al-Mg powders as well as materials capable
of highly exothermic reactions. Both shaker and planetary mills were instrumented to
read out the vial temperature. For the mechanically alloyed powders, the temperature
measurement was useful in establishing different stages of the milling process, e.g.,
38
formation of flake-like particles, breaking down the flakes, and formation of composite
and then alloyed powders [66]. For the exothermically reacting materials, as is common
in reactive milling [67], the temperature jump in the milling vial may show directly and
very clearly when the reaction has occurred.
Mulas et. al [65] employed a piezoelectric transducer and magnetic position
sensor to measure impact frequency, impact time and vial velocity in a single-ball
vibro-mill and a shaker mill. The primary objective was to establish the right amount of
energy and thereby, milling parameters necessary to initiate a self-propagating reaction in
the materials system under consideration.
Iossana and Magini reported electrical and mechanical power consumption
measurements on a planetary mill in their two successive papers [63, 64]. Their work
stemmed from the interest in comparing the theoretical energy consumption in a ball
milling process based on mechanistic collision models to that from experimental power
consumption measurement. The authors established a satisfactory correlation between the
two for a planetary ball mill and suggested that the same concept could be extended to
other devices.
In summary, the utility of the real-time measurements of the consumed power,
vial temperature and some of the other characteristics of the milling process has been
well established. Most successful real time measurements indicated qualitative changes in
the material properties, such as formation or destruction of flakes and occurrence of
39
exothermic, self-sustaining chemical reactions. However, detection of more subtle
changes in the materials properties, e.g., evolution of the particle sizes, development of
the alloyed phases, altering mechanical strength and hardness, has proven to be more
challenging. Most related measurements were performed for specific materials systems
and customized milling configurations. Thus, it remains unclear whether such trends,
identified rather narrowly for specific materials systems and milling devices, are capable
of predicting milling progress for different materials or different milling configuration.
It is also interesting that many related efforts involved shaker and planetary
mills, devices that are very common in laboratory experiments, but not readily scalable
for commercial manufacturing. Conversely, the data on correlations between real time
power consumption and torque and material refinement in the attritor mills are very
difficult to find, whereas attritors are most likely to be used in larger scale production of
new materials. This lack of data for attritor mills is especially surprising considering
that some of the popular commercial attritor mill models, e.g., by Union Process, are
routinely equipped with sensors and a data acquisition board, enabling users to read and
record power, rotation rate, and torque readily.
This project is aimed to establish an experimental foundation for assessing milling
progress while preparing materials in an attritor mill utilizing non-invasive, real time
process indicators. A systematic approach is proposed, relying on simultaneous
measurements of the motor torque, power, and rotation speed (rpm) during preparation of
40
mechanically milled materials. In addition to assessing the milling process parameters
averaged on the time scale comparable to the overall milling time, short-time deviations
of these parameters are also considered to help describing milling dynamics. Such
time-resolved data affected by ongoing changes in the material properties might be
particularly useful when comparing experiments with numerical descriptions of the ball
milling process, e.g., using a discrete element model-based approach [35, 36, 38, 60].
Changes in the time-averaged values of real-time indicators are compared to
changes in the structure and mechanical properties of the milled materials. Two materials
with distinctly different characteristics are selected for this study. Both materials are
metal matrix composites consisting of ductile and brittle components. Selected material
compositions are chemically inert, and hence no new compounds could have formed
affecting the mechanical properties of the products. Therefore, work hardening and
powder morphology evolving as a result of milling were the only parameters affecting
mechanical properties of the prepared composite powders. The brittle components were
chosen to have substantially different hardness to investigate its effect on both the milling
progress and milling parameters measured in real time.
41
3.2 Experimental
3.2.1 Materials
Prepared composite powders included aluminum, as a ductile component, containing
inclusions of one of the brittle components: magnesium oxide or boron carbide. Pure
aluminum powder (-325 mesh, 99.9% pure Atlantic Equipment Engineers) served as a
starting material for the milling. Starting materials for brittle inclusions were magnesium
oxide (-325 mesh, 99% pure, by Aldrich Chemical Company, Inc) and boron carbide
(<10 Micron Powder, 99% pure, by Alfa Aesar). As was shown in earlier experiments
[60, 68, 69], during milling, aluminum does not react chemically with either MgO or
B4C, and the milling yields Al·MgO and Al·B4C dispersion-strengthened composites.
The compositions for both materials included 30 wt. % of the brittle component.
Mechanical properties of the starting components as well as those of the hardened steel
milling balls used in experiments are shown in Table 3.1.
Table 3.1 Material Properties of Pure Powders in Comparison to Milling Media [18]
Property Al MgO B4C Hardened steel
Vicker’s hardness, MPa 167 660 4980 1700-2300
Shear modulus, GPa 25.9 87-124 192 ~80
Poisson’s ratio 0.31 0.36 0.21 0.28
Density, g/cc 2.7 3.75 2.51 7.8
The milling media material (hardened steel) is harder than magnesium oxide but is softer
than boron carbide.
42
3.2.2 Milling Devices and Conditions
An attritor mill by Union Process, model 01HD, was used in this study. The milling vial
volume is 750 mL. It is a stationary vial made of hardened steel. A steel impeller rotating
at an assigned speed agitates the milling balls. The vial was cooled by room temperature
water. Further details on the geometry of the mill can be found elsewhere [60].
Case hardened carbon steel balls of 9.5 mm diameter were used. The ball to
powder mass ratio was 36, powder mass used was 50 g and the rotation speed of the
impeller was 400 rpm. The total milling durations used to prepare the Al·MgO and
Al·B4C composite materials were 4 and 6 hours, respectively. Partially milled samples
were recovered every 1 hour for mechanical and structural characterization. For some
experiments, samples were also recovered and examined in 30-min milling intervals.
3.3 Milling Progress Indicators
3.3.1 Material Characteristics
Various material parameters, including particle size, dimensions of the formed inclusions,
mechanical characteristics, or crystallographic characteristics can be used as indicators of
refinement achieved as a result of milling. In this study, both mechanical and structural
characteristics were exploited. Specifically, yield strength measured while preparing
consolidated powder samples and a width for an aluminum peak in the x-ray diffraction
(XRD) patterns were determined.
43
In mechanically milled composites, the yield strength typically increases as
milling progresses due to formation of dispersion-strengthened materials. The crystallite
sizes decrease when the material becomes more refined, e.g., as a result of a longer
milling time. In the XRD measurements, wider peaks correspond to more refined
materials. Hence, an increase in the peak width with time is expected.
The methodology to obtain the yield strength was presented in section 2.3.2 and
is only briefly outlined here. The powder is compacted in a cylindrical die and the
displacement is obtained as a function of the applied load using Instron 5567. The
compression curves are re-plotted in terms of inverse porosity as a function of pressure;
obtained trends are interpreted using a modified Heckel equation [55], in which yield
strength is treated as an adjustable parameter.
XRD experiments were performed on a Phillips X’pert MRD powder
diffractometer operated at 45 kV and 45 mA using Cu-Kά radiation (λ =1.5438 Å). A
typical pattern for the aluminum-boron carbide sample is shown in Figure 3.1. The peaks
for which the widths are indicated belong to the aluminum XRD pattern (38.5º and
44.5º). The peak width is measured at the level equal to half of its maximum height, also
known as the Full Width Half Max (FWHM). Results for both aluminum peak widths
were consistent to each other, so only the FWHM values for the peak at 44.5º are
presented.
44
2theta, deg
30 35 40 45 50
Inte
nsity,
a.u
.
Peak width
Peak width
Al
Al
B4C
B4C
Figure 3.1 X-ray diffraction pattern for Al·B4C sample recovered from the attritor mill
after 2 hours; the FWHM is marked.
3.3.2 Real time milling progress indicators
A data acquisition system by Baldor is built in the control unit of the Union Process
HD-01 attritor mill. The parameters measured include speed of rotation (rpm), power,
and torque. These measurements, readily available for the attritor mill, were considered
in the present paper. The data were recorded after different milling times in 10-s bursts
with 1 ms time resolution. Figure 3.2 shows typical acquired signals.
45
Time, s
0 2 4 6 8 10
Po
we
r, W
95
105
115
To
rqu
e, N
m
2.0
3.0
4.0
rpm
404
406
408
410
412
Figure 3.2 Real-time milling process parameters recorded for an Al·B4C sample after its
2-hour milling.
3.4 Results
3.4.1 Particle Shapes and Sizes
Powders were recovered every 1-hour for both materials and back-scattered Scanning
Electron Microscopy (SEM) images were taken. The SEM images of samples obtained at
certain milling times are presented in Figures 3.3-3.5 to illustrate the evolution of the
particle shapes. In all of these images, a) corresponds to the Al·MgO and b) is Al·B4C.
Also, the pictures on the left and right in each figure indicate the same sample shown at
two different magnifications (scale shown at the bottom of each image). The milling
times are indicated in the top left corner of each picture.
46
For both materials a qualitatively similar evolution in the particle morphology as
a function of the milling times is observed. It can be broken down into the three steps:
1) Formation of flake-like particles (Figures 3a and 3b for Al·MgO and Al·B4C
respectively)
2) Breaking down the flakes into smaller, more equi-axial fragments (Fig 4a and
Fig4b for Al·MgO and Al·B4C respectively),
3) Agglomeration of the produced fragments into larger particles with relatively
stable sizes. (Figures 3.5a and 3.5b for Al·MgO and Al·B4C respectively)
Figure 3.3a) Al·MgO SEM images of samples recovered after 1 hour of milling.
47
Figure 3.3b) Al·B4C SEM images of samples recovered after 0.5 hour of milling.
Figure 3.4a) Al·MgO SEM images of samples recovered after 2 hours of milling.
48
Figure 3.4b) Al·B4C SEM images of samples recovered after 1 hour of milling.
Figure 3.5a) Al·MgO SEM images of samples recovered after 4 hours of milling.
49
Figure 3.5b) Al·B4C SEM images of samples recovered after 4 hours of milling.
Within this overall sequence, there were important differences between materials
with different compositions. The agglomeration of the broken flake fragments occurred
much sooner for Al·B4C compared to Al·MgO, resulting in the substantially larger
dimensions of the stabilized agglomerates of the former compared to latter. Second, the
surface of flakes and surface of the formed agglomerated particles was relatively
homogeneous for Al·MgO (Figures 3.3a, 3.4a and 3.5a); conversely, inclusions of B4C
were clearly visible at the surface of the Al·B4C composite particles (Figures 3.3b, 3.4b
and 3.5b). Furthermore, unattached B4C were detected in the Al·B4C composite material
until 1 hr of milling (Figure 3.4b), while unattached MgO particles could not be detected
in any of the inspected, partially milled samples.
50
3.4.2 Yield Strength
The yield strengths for both prepared composite powders as a function of milling time are
presented in Figure 3.5.
Al.MgO
Al.B4C
0 1 2 3 4 5 6
Milling time, hrs
40
60
80
100
120
140
160
180
Yie
ld s
tre
ng
th,
MP
a
Figure 3.6 Yield strength for Al·MgO and Al·B4C samples recovered at different milling
times.
Each data point is an average of 6 measurements representing 6 consolidated
pellets for Al·MgO and 3 measurements/pellets for Al·B4C. In both the cases, at very
short milling times the yield strength is small. This is associated with formation of Al
flakes as presented in the SEM images in Figure 3.3, while aluminum is not yet work
hardened. The flakes are readily deformed under pressure, resulting in lower measured
yield strength. As the milling continues, the flakes are broken apart and composite
51
particles form. This is accompanied by an increase in the yield strength. This increase is
substantial for both materials. Also, upon further milling, the yield strength appears to
stabilize for both cases.
3.4.3 X-ray peak width
Figure 3.7 shows the widths of aluminum peaks or FWHM for the two materials as a
function of milling time.
Milling time, hrs
0 1 2 3 4 5 6
Pe
ak w
idth
, d
eg
ree
s
0.3
0.4
0.5
Al.MgO
Al.B4C
Figure 3.7 FWHM for aluminum XRD peak at 44.5º as a function of milling time.
The overall trends in Figure 3.7 show that the peak width increases as a function
of milling time, indicating formation of increasingly more structurally refined materials.
The structural refinement appears to occur from the very beginning of the milling process
and is unaffected by the formation of flakes at short milling times. For Al·MgO, the
refinement of aluminum crystal grains is slower than that for Al·B4C. Also, the final peak
52
width achieved is greater for Al·B4C. These observations are likely explained by a greater
effectiveness of boron carbide inclusions as milling aids accelerating the fracture
propagation in the composite particles as compared to softer inclusions of MgO.
3.4.4 Real-time measurements
The fractions of data presented in Figure 3.2 are shown at an expanded time scale in
Figure 3.8. Changes in power and torque occur in phase with each other whereas changes
in rpm occur in the opposite phase. The main period of the observed oscillations,
approximately 0.15 s, correlates with the period of the impeller’s rotation set at 400 rpm.
At different milling times, average values of the measured power, torque, and rpm
changed, and these changes were explored as possible indicators of the milling progress.
In addition to the change in the average values of the measured parameters, changes in
the amplitudes of their respective oscillations were also noticed. The latter changes were
quantified considering standard deviations of the measured parameters taken over a
period of 10 s.
53
rpm
403
405
407
409
411
To
rqu
e, N
m
2.0
3.0
4.0
Time, s
3.0 3.2 3.4 3.6 3.8 4.0
Po
we
r, W
95
105
115
Figure 3.8 Real-time milling process parameters recorded for an Al·B4C sample after its
2-hour milling (Fig. 2) shown with an expanded time scale.
The processed results of real time measurements for both material systems are
shown in Figure 3.9. The standard deviations in rpm are shown instead of the relatively
stable average rpm values. The standard deviations for torque and power follow trends
similar to the standard deviations for rpm and hence are not shown in separate plots;
however, these standard deviations are represented by the error bars for their respective
average values shown in Figure 3.9.
54
To
rqu
e, N
m
3.5
4.5
0 1 2 3 4 5 6
Milling time, Hrs
Po
we
r, W
95
105
115
125
135
rpm
std
ev
1.0
1.4
1.8
2.2
Al+B4C
Al+MgO
Figure 3.9 Average values and corresponding standard deviations for real-time indicators
measured to assess milling progress as a function of the milling time.
All three parameters tracked, including power, torque, and standard deviation of
rpm, show opposite time-dependent trends for the two materials systems studied. There is
an increase in rpm variations, torque and power for the aluminum-magnesium oxide
system as a function of the milling time; however, the same process indicators
consistently decrease with milling time for the aluminum-boron carbide composite. Also,
55
despite identical milling conditions, the initial values for all three real time indicators are
much higher at the outset for the boron carbide system.
This disparity in the trends between the two materials is likely a consequence of
the different refinement mechanisms in the two powders. This is turn, is attributed to the
difference in properties as shown in Table 3.1 and discussed below.
3.5 Discussion
It is first interesting to directly correlate changes in the powder characteristics, yield
strength and FWHM, with changes in the milling process parameters measured in-situ.
Because measured changes in power, torque, and standard deviation for rpm are well
correlated with one another for each material, as shown in Figure 3.9, only changes in
power are taken for direct comparison with yield strength and FWHM. These correlations
are shown for both materials in Figure 3.10. Please note that vertical scales for power are
different for different materials.
For Al·MgO composite, changes in all three trends, presented in Figure 3.10,
correlate with one another. As the powder becomes more and more refined and work
hardened, the power required to maintain the preset rpm increases, as indicated by the
observed trend. Similarly, harder powder becomes more difficult to compact, as
indicated by the increasing yield strength. The increase in FHWM shows a consistent
structural refinement as a function of the milling time.
56
Milling time, hr
0 1 2 3 4 5 6
0.3
0.4
0.5
50
100
115
120
125
130
135
Pow
er,
W
100
105
110
115
Yie
ld S
trength
,
MP
a
50
100
Milling time, hr
0 1 2 3 4
Peak w
idth
,
degre
es
0.3
0.4
0.5
Al.MgO Al.B4C
Figure 3.10 Changes in power measured in real time during ball milling compared to
changes in parameters of the powder samples (yield strength and FWHM) recovered at
different milling times for Al·MgO and Al·B4C composites.
It is interesting that in Figure 3.10, only changes in yield strength reflect the effect of
flake formation at short milling times. From Figure 3.9 it is apparent that changes in the
standard deviation of rpm reflect this effect as well. Although not shown in separate
plots, changes in standard deviations for torque and power also correlate with the
observed flake formation. Thus, both changes in standard deviations of the milling
parameters measured in real time and change in the yield strength are useful in tracking
the flake formation for this material.
57
For Al·B4C composite, the power is observed to decrease as a function of the
milling time. This may be attributed to the presence of very hard, fine B4C particles
which behave as an abrasive and create significant friction at earlier times during milling.
At longer milling times, when these particles are more and more embedded into Al
matrix, their direct interactions with the milling tools are diminished. Apparently, this
effect is stronger than that caused by work hardening of the produced Al-matrix
composite particles. The yield strength for this powder is also affected by changing
mechanical properties of the composite particles as well as by the changes in the particle
shapes. At early milling times, when flakes are formed, the yield strength increase is
small because of the ease with which the flakes are deforming.
Effect of flake formation on the measured process parameters may be tracked to
the increase in power (and torque, Figures.3.9, 3.10) at the short milling times.
Embedding abrasive B4C particles in Al flakes may have caused this effect. For MgO, the
flake formation occurred simultaneously with fragmentation of the original MgO
particles (not observed in any partially milled samples), while B4C particles retained their
shapes and sizes until much later in the milling process.
The effect of abrasive B4C particles is less noticeable in the slow compaction, so
that the changes in yield strength are dominated by properties of readily deformed Al
flakes, similar to Al·MgO.
58
As soon as the composite particles are produced, the yield strength increases.
Its further changes are similar to that of Al·MgO composite, i.e., due to the formation of
work hardened aluminum with tiny embedded boron carbide particles as observed in
SEM images. However, the measured in real time power and torque decrease; as
mentioned above, likely because of the reduced number of abrasive B4C particles
interacting directly with the milling tools.
A consistent increase in the FHWM shows continuous structural refinement of
the Al-based composite material. The rate of this refinement appears to be higher when
unattached B4C particles are present (shorter milling times). The rate is reduced once
most of the B4C particles are embedded; however, the structural refinement continued
during the entire experiment.
Changes in the motor power measured in real time (and other real time
indicators) as well as changes in XRD pattern as reflected by FHWM and the yield
strength and were found to correlate with the structural refinement in this material.
3.6 Conclusions
Changes in structural and mechanical characteristics of metal-matrix composite materials
prepared by mechanical milling and recovered at different milling times are compared to
changes in the parameters characterizing milling process in real time. For the material
with components softer than the milling media, increases in yield strength and in the
59
structural refinement directly correlated with increases in the motor power, torque, as
well as with increase in the amplitudes of rapid oscillations of the milling process
parameters. Without inspecting the partially milled powders, formation of flakes at early
milling times can only be unambiguously correlated with changes in the amplitudes of
rapid oscillations of the milling process parameters, but not with time-averaged values of
these parameters. For the material with a starting component harder than the milling
media, the abrasive action of the harder starting particles (becoming less significant at
longer milling times) affected the motor power and torque stronger than the hardening of
the prepared composite. Changes in the milling process parameters measured in real time
were found useful in tracking the milling progress, although the reduction in the power
and torque (as opposed to their increase) correlated with the material refinement.
Formation of flakes at early milling times could be correlated with changes in both
time-averaged values of power and torque as well as with changes in amplitudes of rapid
oscillations of the measured milling process parameters.
60
CHAPTER 4
DISCRETE ELEMENT MODEL FOR AN ATTRITOR MILL WITH IMPELLER
RESPONDING TO INTERACTIONS WITH MILLING BALLS
4.1 Introduction
Ball milling is a versatile and scalable technique for processing and preparation of a wide
range of materials, including advanced mechanically alloyed powders [5, 70],
powder-like components of energetic materials [49, 71, 72], materials for energy storage
[73-75], structural applications in aircraft, automotive and military industries [69], etc.
The range of potential applications for mechanical milling as a materials processing
technology is rapidly expanding, including preparation of solid dosage forms in
pharmaceutical industry [76], battery components [77, 78], materials for food processing
[79], artificial bone compositions [16], and remediation of contaminated soil [80].
Despite discovery of many advanced materials that could be prepared by milling,
practical and commercial manufacture of such materials poses significant challenges. In
particular, it is difficult to predict which milling conditions should be used in a practically
scaled milling device to reproduce an advanced material prepared in laboratory
experiments. Such predictions should rely on a validated theoretical description of
material refinement, suitable to describe milling devices of different types and scales.
61
Discrete Element Modeling (DEM) is well suited and has been used extensively
to describe operation of various ball mills, e.g. [39, 40, 50, 81-84]. However, direct
comparisons between the DEM-predicted characteristics of the ball-milling process and
experimental results are not straightforward. One common denominator for both
experimental and computational data is the energy transferred from milling tools to the
powder being milled. Respectively, an energy-based parameter, milling dose, was
introduced as a useful concept in our previous work [35, 36, 60]. The milling dose, Dm, is
defined as the energy transferred from milling tools to the powder, normalized by the
powder mass, mp:
/m d pD E t m (4.1)
where Ed is the rate of energy dissipation from milling tools and t is the milling duration.
It was suggested that the same material could be prepared in different milling devices if
the same starting powders were used and if the same milling dose was transferred to the
material from milling tools. The successful application of this approach depends on how
accurately the milling dose is predicted by DEM descriptions for different milling
devices. For example, if a material of interest is prepared in a small scale shaker mill,
the Dm value can be obtained using the experimental milling time, texp, and a DEM model
quantifying the energy dissipation rate by milling balls in the shaker mill, Ed. This milling
62
dose can now be used to predict the milling time required to prepare the same material in
a different mill, using DEM to appropriately calculate the respective energy dissipation
rate.
The concept of milling dose was explored comparing material preparation in a
shaker, planetary, and attritor mills [60]. The first two mills are common in laboratory
experiments; the attritor is more suited for commercial scale manufacture. Theoretical
models of the milling devices were set-up to obtain the respective Ed terms. In
experiments, the same material was prepared using the same starting powders in each
mill. Respective milling times, t, and mass loads, mp, were recorded. The milling dose
values for the shaker and planetary mills were close to each other, as expected. However,
the computed energy dissipation rate for the attritor was very high, resulting in a much
greater than expected milling dose. It was noted that in the attritor mill computation, balls
were often predicted to jam, resulting in unrealistically strong forces exerted onto the
milling media from the impeller moving at a constant, pre-set speed. These predicted
high-force interaction events result in a substantially over-predicted rate of energy
dissipation, making the respective DEM description inadequate.
In experiments, ball jams can also occur; however, they cause small changes in
the impeller speed. Thus, the variations in the force are attenuated. Santhanam and
Dreizin [60] proposed a screening scheme to account for the computationally predicted
events associated with unrealistically high forces, in which any events involving
63
unrealistically high forces were discarded. The resulting, corrected milling dose for the
attritor was much closer to that predicted for other milling devices.
Although that approach was effective to obtain the desired outcome, a DEM
description that represents the actual operation more directly, without superficial
screening, is desired and developed here. The model enables instantaneous changes in the
rotation speed of the impeller responding to instantaneous changes in the resistance
caused by the milling balls. Recent results on experimental monitoring of rotation rate
and torque in the attritor mill [60] as well as additional experiments are used to tune the
developed model. The predictions of the developed model are discussed in terms of both
accuracy of the assessed energy dissipation and its use for evaluation of the milling dose.
4.2 Materials and Methods
4.2.1 Experimental
Detailed descriptions of the milling conditions, materials and characterization techniques
can be found elsewhere [60], and they are only briefly outlined here. An oxide dispersion
strengthened aluminum-magnesium oxide (Al∙MgO) composite was prepared in three
different mills, including an attritor, shaker and planetary, in order to assess and compare
the milling dose required to prepare the same material in different devices [60]. The same
starting materials, pure aluminum (-325 mesh, 99.9% pure, by Atlantic Equipment
Engineers) and magnesium oxide (-325 mesh, 99% pure, by Aldrich Chemical Company,
64
Inc.) blended at 70%/30% Al/MgO volume ratio were used. The same 9.5-mm diameter
hardened steel milling balls were used in all three mills.
In each mill, the milling balls became coated with the powder and thickness of the
formed coating was assessed experimentally. First, mass of uncoated balls was recorded,
and then the balls coated with the powder were recovered after selected milling times and
weighed. The results of these measurements are shown in Table 4.1 in terms of the
average weight of the powder coating on one milling ball and its standard deviation from
measurements taken at different milling times. The mass shown in Table 4.1 is affected
by both pre-set ball to powder mass ratio and dynamics of ball motion in each mill.
Table 4.1 Average Mass of Powder Coating Per Milling Ball for Different Mills
Milling Device Ball to Powder Mass
Ratio
Mass of Powder Coating per
Milling Ball, g
Shaker Mill 10 0.010±0.009
Planetary Mill 3 0.019±0.011
Attritor Mill 36 0.007±0.005
Yield strength of consolidated powders served as an indicator of the milling
progress and was measured as a function of milling time for the powders prepared in each
mill. The present model focuses on experiments using an attritor mill, model 01HD by
Union Process. In this mill, milling balls are agitated by a steel impeller rotating at a
designated speed. In the experiments, the impeller was set to rotate at 400 rpm. The
attritor mill contains a built-in data acquisition unit by Baldor. It was used to measure the
65
torque and rotation speed as a function of milling time [60]. The mechanical power
required to turn the impeller was calculated from the product of torque and the rotation
speed. The data were collected at different milling times; each collected data set was
recorded for 1 s with a time resolution of 1 ms.
In order to explore the effect of powder properties on the energy dissipation rate,
in addition to experiments with Al∙MgO composites, experiments were also performed
with a powder blend of Al and B4C (70/30 % by volume) and with sand. In experiments
[60], the attritor vial filled with the steel milling balls contained 1.8 kg of balls and 50 g
of powder. Additional experiments were performed, in which the torque and rotation rate
were measured for reduced loads. Specifically, balls were loaded with their masses
representing one half (0.9 kg), one third (0.6 kg) and a quarter (0.45 kg) loads. No
powder was added for these additional experiments.
Friction coefficients necessary for DEM calculations were obtained
experimentally as described previously [60] for the ‘full load’ for different materials. For
the cases when no powder was used, the tabulated friction coefficients for the plain steel
ball rolling on steel vial surface were used. The values of the friction coefficients
characterizing different materials are shown in Table 4.2.
66
Table 4.2 Friction Coefficients Characterizing Different Milling Configurations
Material System Static Friction
Coefficient
Rolling Friction
Coefficient
Steel (no powder) 0.25 0.01
Al∙MgO 0.30 0.05
Al∙B4C 0.34 0.07
Sand 0.60 0.09
Torque and rotation rate measured in real time for partially loaded vials and for
the fully loaded vials with the Al∙MgO blend are shown in Figure 4.1. The torque is
increasing with the increased vial load. The change is most substantial when the load
increases from ½ to full load. In addition, oscillations in the recorded torque become
stronger as the load is increasing. Similarly, stronger oscillations are observed for the
rotation rate at increased loads. The average rotation rate remains unaffected for , ,
and loads; however, it decreases slightly when the full load is achieved.
67
Time
Torq
ue
, N
m
2
3
4
5
6
Rota
tion s
peed,
rpm
400
402
404
406
408
410
1/4 Load 1/3 Load 1/2 Load
Full Load
1 s
Figure 4.1 Torque and rotation rate measured in experiments with different vial loads.
4.2.2 Model
EDEM, a commercially available DEM code by DEM Solutions was used to describe the
attritor mill in this work. The model parameters are briefly mentioned here and detailed
descriptions can be found elsewhere [60]. Hertz-Mindlin (no-slip) contact model was
used to describe particle-vial, particle-impeller and particle-particle interactions. The time
step for simulations was 1 μs and data were recorded every 100 µs. Material properties
corresponded to the actual materials used. The static and rolling friction coefficients for
the milling balls coated with the powder being processed were determined using
additional experiments [60], see Table 4.2. EDEM, as well as other DEM codes, solve
equations of motions for particles, i.e., milling balls in this simulation. The motion of
68
“geometry elements”, i.e., milling vial and impeller, is pre-defined by the setup and is not
adjustable in response to interactions between “particles” and “geometry elements.”
The issue of defining a DEM approach to describe response of a rigid body upon its
interaction with particles has been discussed in the literature [85, 86] However, this issue
has not been addressed for the present attritor mill configuration.
Short of modifying the entire DEM code, in this work, the attritor’s impeller was
modeled as a large, complex shape particle, or cluster of particles as shown in Figure 4.2.
The impeller is constructed using 12.72 mm spherical particles spaced within 2 mm to
one another, so that a nearly smooth surface is achieved. The length of the impeller is 140
mm. There are four side-arms, each is 64-mm long. A total of 216 fused particles are
used to construct the impeller. Once the particles are positioned together to create the
desired shape, contact forces are not generated between these individual particles. This
technique of ‘fusing’ spherical particles together to create particles of complex shapes has
also been reported elsewhere [87-90]. The impeller is inserted into the vial through an
opening in the vial’s lid. The diameter of the opening is 16.7 mm. Since the impeller’s
diameter is smaller than that of the opening (as is the case for the actual mill), the
impeller can tilt and move horizontally.
69
Figure 4.2 Model description of the vial with impeller.
In the actual mill, the impeller is mounted in a motor transmission system, so its
effective inertial response to interactions with the milling balls is affected by the way it is
mounted. To imitate the impeller’s inertial response in the code, its mass was varied
systematically. Figure 4.3 shows schematically three impeller designs considered.
70
Design A B C
64
12.72
Vial
16.7
76
102
89
Figure 4.3 Schematic diagrams of impellers with different masses. A, B, C are
respectively the impellers with its actual mass, double, and triple mass.
In case A, the impeller in the code simply reproduces the dimensions of the actual
impeller. In case B, a metal cylinder is added at the top of the impeller. This added
cylinder’s dimensions are selected so that the mass of impeller B is twice that of impeller
A. Similarly, in design C, the added cylinder results in the overall mass to be triple that of
A. The cylinders added on to the impellers B and C also comprise of fused spherical
particles.
The impeller was moved by an applied torque. The torque was varied depending
on the rotation speed, the variation was determined based on experimental data. It was
observed that in experiments, instantaneous values of torque and rotation speed change in
71
the opposite phase [60], see also Figure 4.1. The data collected previously [60] was
re-processed to establish an overall correlation between the measured torque and rotation
speed, as shown in Figure 4.4. A linear fit for the observed experimental trend is also
shown. This fit was used in the code to describe the impeller motion.
Impeller rotation speed, r, rpm
403 404 405 406 407 408 409 410 411 412
Torq
ue,T
, N
m
2.0
2.5
3.0
3.5
4.0
4.5
Fitting Model:
T=-0.2.r+86.31
Figure 4.4 Relationship between torque and rotation speed of impeller as obtained from
real-time measurements.
Data shown in Figure 4.4 also indicate the range of practically observed changes
in the rotation speed and torque during the mill operation. In preliminary calculations, it
was observed that the impeller can still be jammed, causing much greater instantaneous
changes in its rotation rate compared to data in Figures 4.1 and 4.4. To avoid this
situation, the impeller’s motion was finally described as follows:
72
403 ; 100
403 ; 0.2 86.3
rpm T Nm
rpm T Nm
(4.2)
Where ω is the impeller rotation speed and Τ is the torque.
An increase in the torque for the rotation rate below the observed range (ca. 403
rpm) describes the response of the transmission system that maintains the rotation rate in
the mill. The value of 100 Nm is selected after testing higher and lower torque values and
observing the resulting predicted range of rotation rates. For lower torque values, the
return of the rotation rate to the pre-set range occurred slowly; higher values of torque
resulted in instantaneous acceleration of rotation rate above the experimental range.
4.3 Results
The overall range of rotation rates and torque values produced by the DEM description
correlated well with the experimentally observed ranges, as illustrated in Figure 4.5.
For this preliminary comparison, the calculations represent impeller described by design
A in Figure 4.3. The data are presented for a 1-s interval. The experimental data were
acquired with a time resolution of 1 ms. In the calculation, the data were saved every 0.1
ms; then the average of 10 points was used to reduce the time resolution to 1 ms to be
directly comparable with experiments.
73
Time, s
1.0 1.2 1.4 1.6 1.8 2.0
Po
wer,
W
101
102
103
Imp
ell
er
rota
tio
n
rate
, rp
m
404
406
408
410
412Experiment
EDEMT
orq
ue,
Nm
10-1
100
101
Figure 4.5 Calculated and experimental instantaneous values of rotation rate, torque, and
power. Impeller design A (Figure 4.3) was used in calculations.
The experimental trace (similar to that shown in Figure 4.1) appears to exhibit
oscillations with both high and low frequencies. The period of the low frequency
oscillation is close to the time of one full rotation for the impeller. It is difficult to
interpret the high-frequency oscillation because it is only weakly depending on the load
of the milling vial. In other words, the high frequency pattern is observed even for the
74
empty ball mill. The DEM prediction shows only a relatively high frequency oscillation
pattern.
The power dissipated by the milling tools was also compared for experimental
data and predictions. For experiments, the mechanical power was calculated as a product
of the torque and impeller rotation speed. In the model, power was obtained directly as
the sum of energies dissipated in individual collision events per second. In both cases, the
power characterizes the rate of energy transfer from milling tools to the powder.
The comparison between the experimental and calculated power values is shown
in Figure 4.5. The instantaneous changes in both values are significant; however, the
changes occur in the same range, suggesting that the calculations are generally consistent
with the experiments.
The average and standard deviation data for power as obtained from experiments
and DEM models A, B, and C are shown in Figure 4.6. The variation in experimental
load was described previously. A power increasing with the load was observed in
experiments and was well reproduced in the model. The influence of both load and
impeller design on both the predicted power and the range, in which it varies, is observed.
The average values of power are shown in the top plots and standard deviations are in the
bottom. The best match of experimental and computed data is observed when double
impeller mass (design B) is used in the DEM model. It is interesting that the match
improves simultaneously for both the average power value and for its standard deviation.
75
Avera
ge p
ow
er,
W
1
10
1001/4 load 1/3 load 1/2 load
Full loadS
tandard
Devia
tion,
W
1
10
100
EDEM
Experiment
Impeller designs: A: regular mass; B: double mass; C: triple mass
A B C A B C A B C A B C
Figure 4.6 Results of parametric investigation: average power and its standard deviation
at different vial loads for model and experiment. The model results are shown for three
impeller designs A, B and C.
The range of power variation (expressed through standard deviation in Figure 4.6)
is systematically greater for the model compared to experiments. The difference appears
to increase at higher loads. It is likely that this discrepancy of calculations and
measurements is caused by the finite time resolution of the experimental data acquisition
system, compared to the instantaneous capture of the torque and rotation rate values in
the DEM output.
76
To understand why design B exhibits the best match with experimental data in
Figure 4.6, the impeller’s motion for each design was examined further. Locations of the
bottom tip of the impeller as a function of horizontal coordinates, X and Y are shown in
Figure 4.7. Each data point represents a position of the impeller’s tip at an individual time
step during the simulation. The data are shown for a simulated time of 1 s.
Design A
-4 -2 0 2 4
Y, m
m
-4
-2
0
2
4
X, mm
-4 -2 0 2 4 -4 -2 0 2 4
Design B Design C
Figure 4.7 Horizontal coordinates of the bottom tip of the impeller for designs A, B, and
C.
It was observed that the impeller by design B is generally more confined in space
compared to both designs A and C. It can be qualitatively explained as follows. When a
lighter impeller (design A) is used, its position is strongly affected by the interactions
with milling media and it is displaced from its central location easily. On the other hand,
in a much heavier design C, the impeller’s inertia is high. Thus, once displaced, it takes a
long time to return to the central position. Design B appears to result in the most confined
and realistic motion pattern, also yielding the best match between experimental and
predicted energy dissipation rates.
77
4.4 Discussion
4.4.1 Predicting Power Dissipation
A direct DEM validation can be obtained if the power dissipated during milling is
predicted accurately for preparation of different materials. The effect of material is
included in the DEM through adjustment of the directly measured restitution and friction
coefficients [60]. Comparisons of the present “responsive” impeller model with the
experimental data collected during milling three different materials: Al∙MgO and Al∙B4C
composites, sand, as well as operation of the mill with milling balls only [60] are shown
in Figure 4.8. The friction coefficients shown in Table 4.2 were utilized in the
calculations. The model employed impeller design B.
Po
we
r, W
0
50
100
150
200
250
300
Al.MgO Al.B4C SandSteel
DEM (Design B)
Experiment
Figure 4.8 Comparison of average and standard deviation in powder from EDEM and
experiments.
78
The match between the predicted and measured power is good for all cases. The
error bars show standard deviations from the average value for both calculations and
measurements taken for 1 s, which was the time of data acquisition in both experiments
and computations. A greater error bar observed for the predicted values of power is, as
earlier mentioned, likely associated with a higher time resolution obtained in calculations
compared to experiments. Comparisons shown in Figure 4.8 validate the present DEM
description of the milling in an attritor and show that the energy dissipation from the
milling tools is predicted accurately.
4.4.2 Evaluation of the Milling Dose
Using design B, for which, as shown in Figure 4.8, the energy dissipation in the attritor is
accurately predicted, the milling dose was reevaluated for the experimental conditions
used previously [60]. The material prepared in those experiments was Al∙MgO composite
powder; different powders prepared using different milling devices were assumed to be
identical if they exhibited the same yield strength. Because the same powders were
prepared using different mills, it was anticipated that an accurate model would yield the
same milling dose for each of the milling conditions. However, this was not the case for
the attritor, as discussed in more detail previously [60].
79
It was established that ball jams resulted in unrealistically high forces leading to
substantially overestimated rate of energy dissipation in the attritor. To identify the issue,
individual collision events in the milling vial were sorted based on the average force
exerted in these events. The results are shown in Figure 4.9. The data for shaker,
planetary and attritor mill presented earlier [60] are shown for reference.
Average force, N
10-5 10-4 10-3 10-2 10-1 100 101 102 103 104 105
Inte
raction e
ve
nts
(co
llisio
ns)
100101102103104105
100101102103104105
Shaker1054 rpm
101102103104 Planetary:
350 rpm
Filtered outAttritor: 400 rpm
"Responsive" impeller
Figure 4.9 Histograms sorting interaction events of milling tools based on the average
force for different milling devices.
For the attritor mill, the energy dissipation rate predicted considering the constant
rotation rate of the impeller was previously manually filtered to remove the high force
events, falling into the shaded region in Figure 4.9. An overlapped histogram shows data
from the current “responsive” impeller model. The very high force “tail” for the attritor
80
mill disappeared, so no superficial data filtering is necessary. On the other hand, more
interaction events with lower forces are observed. Estimates suggest that such low-force
events do not result in a substantial increase in the overall energy dissipation by the
milling tools and are, therefore, unimportant for assessing the milling dose.
The milling dose values calculated for different mills for the experiments [60] are
presented in Table 4.3. The calculations for shaker and planetary mills as well as the
“unscreened” and “screened” values obtained for the attritor with impeller rotating at a
constant rate were reported earlier. The energy dissipation term (obtained from the
model) used to determine the milling dose is an average over five consecutive time
intervals of 100 ms each. The milling dose for the “responsive” impeller obtained in the
present calculations is close to its “screened” value and thus represents the experiments
reasonably well, without the superficial screening.
Table 4.3 Comparisons of Milling Dose and Associated Parameters for Three Milling
Devices
Parameter Shaker
mill
Planetary
mill
Attritor mill
Unscreened Screened "Responsive"
EDEM model
Ed/mp, W/g 4.6±0.1 2.0±0.04 10.0±1.0 1.7±0.1 1.9±0.2
Experimental
milling time, t, hr 0.4±0.1 1.0±0.3 1.8±0.1
Milling dose, Dm,
W∙hr/g 1.8±0.5 2.0±0.6 18.0±2.8 3.06±0.3 3.4±0.4
81
Despite removal of the unrealistically high forces, the milling dose implied by the
DEM predictions and experiments [60] for the attritor remains somewhat higher than for
the other two mills. In defining the milling dose, the energy dissipation rate predicted by
DEM is distributed over the entire powder load, as shown in Equation (4.1). However, it
is possible that the mechanical refinement in real time occurs just for the powder coated
on the milling balls and the vial surface. This involves only part of the powder, which can
be established using data from Table 4.1. Clearly, the coating is being removed and
re-applied continuously during milling, so that eventually all the powder gets refined.
However, the efficiency of mechanical refinement may depend on how much powder is
coated on the milling tools instantaneously. This correction can be significant for the
attritor, in which the ball to powder mass ratio is much greater that in the other mills
(Table 4.1), so that a greater fraction of powder may be continuously refined. To explore
this hypothesis, an alternative milling dose ( ) definition was considered,
* /m d cD E t m (4.3)
where mc is the mass of the powder coated on the surface of milling tools (including the
surface of the milling vial). The value of mc was calculated for each case considering
mass of coating on an individual ball and assuming that the coating thickness is uniform
throughout.
82
Deriving from previous knowledge of the mill operation in different devices, the
surface area of vial geometry used to calculate mc was different for the three cases. For
the planetary mill, the primary material processing is a result of rolling along the surface
of the vial and hence, surface area of vial walls was used. In the shaker mill, the
collisions on the top and bottom of the vial are important and hence, surface area of the
vial wall as well as top and bottom vial surfaces were included. In the attritor mill, the
powder processing is independent of the top lid surface and hence, the vial walls and
bottom surface were used. The values of and mD for different mills are shown in
Figure 4.10.
Dm
, W
. hr/
g
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Dm
*, W
. hr/
g
0
10
20
30
40
50
60
Shaker Planetary Attritor
Figure 4.10 Milling dose predicted based on the entire powder load, Dm, and an
alternatively defined milling dose Dm*
defined based on the mass of the powder coated
onto the milling balls.
83
The responsive impeller model was considered for the attritor mill. As expected,
because of a greater fraction of the powder coated on the milling tools in the attritor, the
resulting value of D* is reduced and becomes closer to those for the other two mills. It is
apparent that the match between different mills is improved. Note that the error bar for
takes into account substantial error in the measured coating thickness shown in Table
4.1.
Milling dose defined by Equation (4.2) does not directly account for the rates of
coating removal and re-applying during the milling and thus may need to be refined
further. However, the approach taking into account the powder coated onto milling
tools may be useful for more accurate predictions of the milling progress in different
types of mills.
4.5 Conclusions
The accuracy of DEM representation of material processing in an attritor is significantly
improved when interactions of the moving impeller and the milling balls are accounted
for by enabling the impeller to instantaneously slow down when the balls jam, and then
return to its pre-set rotation rate. It is shown that in the model, the rotation of such
“responsive” impeller can be described using an experimentally obtained correlation
between instantaneous values of torque and rotation rate. This correlation can be
programmed into DEM to describe the torque applied to the impeller for the range of
84
rotation rates observed experimentally. When the rotation rate falls below the
experimental range, the torque needs to be further increased.
It is also shown that the mass or moment of inertia of the responsive impeller is
affecting its predicted motion pattern and the energy dissipation rate for the entire system.
Parametric analysis established the specific mass for the impeller for the present
laboratory scale attritor, for which DEM provides the best correlation with the
experimental data. This mass used in DEM accounts best for the way the impeller is
mounted and connected to the motor in the actual mill; similar parametric analysis would
be necessary to describe responsive impellers in different attritor mills.
The DEM employing responsive impeller is accurately predicting energy
dissipation rates for milling different materials when the accurate values of restitution and
friction coefficients are included. Such values can be obtained from separate simple
experiments for each type of material.
Considering responsive impeller, no superficial filtering for the DEM results are
required to predict a reasonable milling dose for the powder prepared in attritor as
compared to the same powder prepared in the shaker and planetary mills. The definition
of the milling dose may need to be corrected to account for the fraction of the powder
coated onto the milling tools, rather than the entire powder charge in the vial.
85
CHAPTER 5
INTERACTION PARAMETERS FOR DISCRETE ELEMENT MODELING OF
POWDER FLOWS
5.1 Introduction
Discrete Element Modeling (DEM) [58] is gaining recognition as a valuable tool
elucidating phenomena occurring on the scale of individual particles in powder systems.
Current research ranges from modeling of particulate flow in hoppers [91, 92] and mixers
[93, 94], describing mills [60, 95, 96], fluidization [97, 98], particle packing studies such
as compaction [99, 100], as well as conveying operations [101, 102]. Despite the broad
appeal of DEM, a significant caveat exists. In order to describe the experimental
phenomena accurately, the model must use the correct particle interaction parameters.
For most DEM codes, these parameters include coefficients of restitution and friction for
particle-particle and particle-wall interactions.
Both collision and friction phenomena are widely studied for macroscopic bodies,
including spherical particles of different dimensions. Coefficients of restitution were
reported based on experimental sphere-sphere collision by multiple authors, e.g., Refs.
[103], [104], [105], [106], and [107]. The materials studied range from polystyrene, glass,
stainless steel to granite balls. However, even the smallest ball size of about 2.5 mm [104]
is still much greater than the typical particle size in most powders.
86
Several studies reported that the restitution coefficient becomes greater for lower
impact velocities [103, 107, 108]; conversely, it was also suggested that its dependence on
velocity is weak [104, 105, 109]. The effect of impact velocity may be important for
powder systems, where relative particle velocities are reduced because of the collective
powder flows.
Although designing experiments to directly monitor collisions of micron level
particles is difficult, theoretical efforts [110, 111] show that the mechanisms governing
energy dissipation in collisions alter for smaller particle sizes. Hence, values of
coefficients of restitution determined in experiments with macroscopic bodies may not be
describing appropriately collisions of much finer particles.
Defining both rolling and static friction coefficients is required for state of the art
DEM codes, such as EDEM [56, 60]. The values for powders are typically obtained from
experimental shear cell [112-114] or compaction studies [115, 116], empirical correlations,
conventional practice, or tailored in the model to match experimental data. Shear cell and
compaction measurements yield generic “wall friction” and “internal friction” values,
which are difficult to relate directly to the rolling and static friction coefficients employed
in the DEM particle interaction models.
Since friction is defined by the surface roughness, asperities, and defects, that may,
for bulk materials, be comparable in size to the dimension of powder particles, the physics
governing friction forces for individual powder particles may be changing [117]. No
87
direct friction measurements for fine particles could be found in the literature, leaving the
data implied by the bulk friction coefficients as a reasonable preliminary assessment for the
static friction. Also, no data could be found for measured rolling friction coefficient. In
several papers [118], [119], [120], empirical correlations were proposed expressing the
rolling friction coefficient as a function of the particle diameter. These correlations are
summarized in Table 5.1. The proposed reduction in the rolling friction for finer particles
might be associated with the respectively reduced size of surface asperities.
Table 5.1 Rolling Friction Empirical Correlations maxrolling X D
X [1/m] Particle Diameter, Dmax [m] Reference
0.001 N/A [118]
0.01 0.0118-0.014 [119]
0.015 0.02 [120]
A set of focused, systematic studies of the effect of particle interaction
characteristics on DEM-predicted powder flow was reported by Ketterhagen et. al [92,
121, 122]. Unfortunately, it was concluded in Ref. [121], that similar results could be
predicted using various combinations of friction coefficients. It appears that the above
conclusion suggests that the experimental data available were inadequate to properly
“calibrate” the DEM and thus identify the true particle interaction characteristics.
88
This work offers an approach for such a calibration combining simple experiments and
their DEM representations. There are two essential features in the present approach:
The experimental system includes a relatively small but statistically significant
number of narrowly sized, spherical powder particles (20,000), so it can be
completely described by DEM.
Experiments with the same powder are performed with systematically varied
powder flow parameters; each experimental configuration is also represented
computationally, which enables simultaneous adjustment of unknown
coefficients of friction and restitution.
5.2 Experiments and Materials
5.2.1 Experimental Setup
A vibratory powder feeder with a miniature hopper was designed as illustrated in Figure
5.1. The hopper size was selected to fit approximately 20,000 50-µm diameter spherical
particles to enable a description of the entire system by a DEM code. Respective
powder mass can vary in the range of 2.6 to 7.9 mg, for powder densities of 2 - 6 g/cm3.
The hopper was built using several inserted miniature brass tubes, as shown in Figure 5.1.
The tubes were soldered on the outside.
The hopper’s outlet was inserted into a horizontal tube through which an air was
flown. Thus, the particles falling out from the hopper were carried away by the air. The
entire assembly was rigidly mounted on the diffuser of a loudspeaker. The loudspeaker
was powered by an amplified signal from a frequency generator. Powder feed rates were
measured at different frequencies: 120, 240, and 500 Hz.
89
The powder was loaded into the hopper before starting the experiment; however,
it did not fall out until the hopper was vibrated. Both the hopper and powder were dried at
a reduced pressure of about 0.2 atm and at 75 °C before each experiment. The hopper was
typically dried for 2 hours and the powder was dried for at least 48 hours. The hopper
assembly was weighed before loading; it was also weighed before and after each
experiment. A Mettler Toledo AX 205DR Delta Range balance was used with the mass
resolution of 0.01 mg. Therefore, the loaded powder mass and powder mass remaining in
the hopper were determined.
Figure 5.1 Schematic of experimental set-up. In the inset, all dimensions are in mm.
90
The air jet carrying particles that fell from the hopper was illuminated by a laser sheet. A
photomultiplier tube (PMT) equipped with a collimator was positioned to detect the light
scattered by the particles passing through the laser sheet. The angle between the incident
and scattered light beams was selected to be 120º optimized for Mie scattering [123].
The PMT output was fed to an oscilloscope. Thus, light scattering peaks produced by
individual powder particles were recorded.
A typical sequence of recorded light scattering pulses is shown in Figure 5.2. In
this example, eight pulses occur during 100 ms, indicating an average feed rate of 80
particles per second.
Figure 5.2 Typical PMT measurement
5.2.2 Vibration Characteristics
The amplitude of vibration was measured using photographs of the exit tube, rigidly
connected to the hopper. A Casio Elixir EX-FH 25 camera with a custom close-up lens
was used to obtain a magnified image of the exit tube against a white background. The
images were taken without and with tube vibration using different pre-set frequencies.
The exposure time was always selected to exceed the period of vibrations. An image of
Scan duration: 100 ms
91
motionless tube was then overlapped with that of a vibrating tube, using ImageJ
processing software, as illustrated in Figure 5.3.
Figure 5.3 A photograph of a motionless exit tube (left) and a mirror image of the
overlaid images of the vibrating and motionless tube (right). The gray band shows the
displacement of the tube edge used to estimate the amplitudes for modeling studies.
The difference between the edge positions in the overlapped images shows the
maximum amplitude of vibration. Positions of the bottom edge of the tube, where the
focus was better, were monitored and used to estimate the amplitudes. Five consecutive
images were taken for the duration of 1 s while the hopper was vibrating. Each image
was used to obtain a data point. It was observed that although most amplitude
measurements performed at each frequency setting were consistent to one another, there
were outliers for some cases, typically showing lower amplitude. The average values
from the consistent data points were calculated and entered as the amplitude in the model.
Table 5.2 presents the average measured amplitude values which were used in EDEM for
the three frequencies.
92
Table 5.2 Vibration Amplitudes for Different Frequencies Obtained from the Image
Processing
Frequency, Hz Amplitude, mm
120 0.31
240 0.16
500 0.10
Although outliers were ignored for the purpose of calculating the average
amplitude, they could have been indicative of a modulated output from the speaker. To
test this, sound waves were recorded using a microphone and visualized using Matlab as
shown in Figure 5.4.
Am
plitu
de
(A
. U
) 240Hz
500Hz
120Hz
1s
0.3s
0.1s
Figure 5.4 Sound waves recorded at different frequencies.
93
Fourier transforms were obtained for each of the recorded waves, showing that
each signal contains four basic waves. Two of these basic waves were comparably strong;
while two others were rather weak. The frequencies and amplitudes of the two stronger
waves were recorded.
To model the modulated signal, two waves were superimposed over each other in
DEM. The strongest wave represented the pre-set frequency with its initial amplitude, as
shown in Table 5.2. The amplitude and frequency for the second wave were calculated
considering the ratios between amplitudes and frequencies of the two strongest basic
waves obtained in the Fourier transform for each recorded sound signal. A comparison of
the experimental and modulated two-wave oscillation used in DEM is shown in Figure
5.5 for a nominal 120 Hz case. It appears that the pattern used in the DEM follows
closely the experimental vibration pattern.
Time, s
0.00 0.05 0.10 0.15 0.20
Am
plitu
de
, m
m
-0.8
-0.4
0.0
0.4
0.8Sound Wave
EDEM Wave
Figure 5.5 Sample wave match for EDEM based on experimental measurement
(120Hz).
94
Results obtained with both single mode sinusoidal oscillations with pre-set frequencies
and modulated waves including two stronger basic waves are presented and discussed.
5.2.3 Materials
The material used in this study was yttrium stabilized zirconia beads (Tosoh USA, Inc.)
with the nominal size of 50 μm. A scanning electron microscopy (SEM) image of the
beads is shown in Figure 5.6. Multiple SEM images were taken and diameters of zirconia
spheres were measured.
Figure 5.6 SEM image of Zirconia beads.
In total, 323 particles were processed and the obtained relatively narrow particle size
distribution is shown in Figure 5.7. This distribution was used in DEM in addition to the
cases describing a monodisperse, 50-µm powder.
95
Diameter, µm
30 35 40 45 50 55 60 65 70
Num
ber
of
part
icle
s
0
50
100
150
200Number of particles processed: 323
Figure 5.7 Size distribution of Zirconia beads (from SEM image processing).
5.3 Model
Commercially available DEM software, EDEM (DEM Solutions Inc.) was utilized in this
research [56]. The Hertz-Mindlin (no slip) soft particle contact model was used for the
force calculations. This model combines Hertz's elastic theory for the normal contacts
and Mindlin's solution for the tangential contacts [58]. Further details can be found in
Ref. [60].
The hopper geometry (brass) and the particles (zirconia) were described by
EDEM. The properties of the brass and zirconia were obtained from literature [124]. The
properties required in the model include density, shear modulus and Poisson’s ratio. Both
mono-disperse particles (with the diameter of 50 μm) and the particle size distribution
shown in Figure 5.7 were considered.
96
The calculations were aimed to establish the values of coefficients of restitution and
friction, for which predicted and experimental powder feed rates match each other at
different hopper vibration frequencies. As a starting point, the values of restitution
coefficient and friction coefficients for the particle-wall interactions were taken from an
earlier work [125]. The initial values of friction coefficients for particle-particle
interactions were evaluated using larger zirconia spheres and following an experimental
method outlined in Ref. [60]. The starting values of coefficients are shown in Table 5.3.
Table 5.3 Initial Values of Restitution and Friction Coefficients Used in EDEM
Interaction Friction Coefficient Restitution
Coefficient Static Rolling
Particle-Particle [60] 0.7 0.03 0.5
Particle-Wall [125] 0.3 0.1 0.5
5.4 Results
5.4.1 Experimental Results
At least six experiments were performed for each pre-set vibration frequency.
Measured feed rates are shown in Figure 5.8. A hashed bar shows the experimental
number of particles per second obtained using the measured mass change of the hopper
before and after the test divided by the time the powder was being fed. For this estimate,
it was assumed that particles were mono-sized, with 50 µm diameter and density of
5.68 g/cm3, corresponding to zirconia. A solid bar shows feed rates obtained using direct
97
peak counts from the recorded oscilloscope traces. Each peak corresponded to one
particle. The feed rates are based on counting 300 – 500 pulses for each pre-set vibration
frequency. The two measurements are in good agreement with each other.
120 500
Dis
ch
arg
e R
ate
, s
-1
0
200
400
600
800
1000
240
Frequency, Hz
From mass
From PMT peak counts
Figure 5.8 Comparison of discharge rates estimated from the hopper mass change vs.
that inferred by the counted PMT peaks.
At 120 Hz, the particles were fed at a consistently low rate. At 240 Hz, the feed
rate increased markedly. At 500 Hz, the feed rate was reduced. In the latter case, it was
noted that the powder always jammed after a period of time. Once a jam occurred, the
powder flow could not be resumed, even if the oscillatory pattern was disrupted by
varying the signal frequency and amplitude. The maximum duration of an individual
experiment was 3.2 min; however, if a jam occurred, the feed rates shown in Figure 5.8
were calculated accounting only for the time before the jam, typically less than 2 min.
98
The average percentages of the powder removed from the hopper in individual
experiments determined from the hopper weighing before and after tests are shown in
Figure 5.9. More than 90% of the particles were removed from the hopper at 120 Hz.
The amount of powder removed at 240 Hz is also close to 90 %. At 500 Hz, only about
50% of the powder was removed from the hopper before it jammed.
Frequency, Hz
0
20
40
60
80
100
Pe
rce
nta
ge
Exite
d, %
120 240 500
Figure 5.9 Percentage of powder removed from the hopper in vibration runs using
different frequencies.
5.4.2 Predicted Powder Motion Patterns
Results of preliminary calculations using friction and restitution coefficients given in
Table 5.3 are illustrated in Figure 5.10. Each simulation described 0.1 s of real time and
considered 20,000 of 50-µm diameter zirconia particles. For each frequency, five images
are selected showing different instants of the simulation.
99
Figure 5.10 Frames from EDEM illustrating motion patterns of particles inside the
hopper for different frequencies. The particle velocities are color-coded.
100
The cup seen in the image (into which the particles are discharged) is a feature of
the model and is not present in the actual experiment, where particles are removed by an
air flow. The color scale represents velocity, red being the maximum and green the
minimum for each simulation. At 120 Hz, the particles appear to closely follow the
hopper motion collectively. At 240 Hz, the powder bed begins fluidizing. Finally, at
500 Hz, well-fluidized motion patterns are observed; there are significant differences in
the particle velocities throughout the sample.
Particle velocity histograms are shown in Fig. 11. Velocities of individual
particles were saved at each sampling interval (0.01 s) during the entire simulation time
(0.1 s). The histograms represent the data integrated over the entire simulation. The
initial simulation period (0-0.01 s) was provided for the particles to completely settle
down and hence, the velocities at this time were not considered for this processing. The
values of velocities are relatively low (compared to several m/s typical for interaction of
macroscopic bodies, such as milling balls [103]). For 120 Hz, there are several
narrowly defined spikes corresponding to velocities less than 0.5 m/s. This pattern is
likely to represent collective motion of the powder interacting with the vibrating hopper.
A qualitatively similar velocity pattern is observed for 240 Hz. For 500 Hz, the velocity
distribution changes substantially. Instead of discrete narrow peaks, a broader
distribution is observed, indicative of substantial energy exchange among individual
101
colliding particles. This change in the velocity pattern is consistent with the appearance
of the fluidized powder in Figure 5.10.
Velocity, m/s
0.0 0.2 0.4 0.6 0.8 1.00
3000
6000
0
20000
40000
60000
Indiv
idu
al P
art
icle
s
0
20000
40000
120Hz
240Hz
500Hz
Figure 5.11 Velocity histograms for individual particles obtained from EDEM.
5.4.3 Sensitivity of DEM Predictions to Coefficients of Restitution and Friction.
Three interaction parameters, including coefficients of rolling and static friction, µr and
µs, respectively, and coefficient of restitution, CR, need to be defined for both
particle-particle (PP) and particle- wall (PW) interactions. Thus, a total of six parameters
(cf. Table 3) should be identified. The following calculations are aimed to establish
how important is the selection of each individual interaction parameter for the prediction
of the powder flow rate. Predicted results are compared to one another, whereas
102
comparison with experiments is discussed later, after the effects of particle size
distribution, amount of powder, vibration pattern, and amplitude are considered. A
comprehensive list of all the simulation runs is presented in Table C.1 in the appendix.
5.4.3.1 Restitution Coefficient
The effect of CR on the predicted powder discharge rate is illustrated in Figure 5.12. For
these calculations, the oscillation frequency was taken as 240 Hz and 20,000 of
mono-dispersed particles were considered. Coefficients of restitution and friction were
the same for both PP and PW interactions for each calculation. It is observed that for low
values of CR<0.5, its effect on the discharge rate is relatively small. However, for
CR > 0.5, its increase results in a substantial growth in the predicted discharge rate. A
qualitatively similar effect of CR on the discharge rate was also observed for other
frequencies and values of µs and µr.
Dis
ch
arg
e R
ate
, s
-1
0
400
800
1200
1600
CR =0.05 0.950.5
µs =0.01
µr =0.001
Figure 5.12 Effect of coefficient of restitution; vibration frequency 240 Hz (Runs 1-3,
Table C.1).
103
A relative effect of CR for PP and PW interactions is illustrated in Figure 5.13. A
reduction in CR for either of the individual PP or PW interactions results in a substantially
lower predicted discharge rate. The effect of PP interactions appears to be somewhat
stronger.
Dis
ch
arg
e R
ate
, s
-1
0
400
800
1200
1600
PP: CR =0.95
PW: CR =0.95
CR =0.95
CR =0.05
CR =0.05
CR =0.95
µs =0.01
µr =0.001
Figure 5.13 Effect of coefficient of restitution: particle vs. wall interactions; vibration
frequency 240 Hz (Runs 3-5, Table C.1).
5.4.3.2 Friction Coefficient
Effect of changes in the values of µs and µr on the discharge rate is illustrated in
Figure 5.14. The value of CR=0.5 for both PP and PW interactions. As earlier, 240 Hz
vibrations are considered for 20,000 of mono-disperse particles. The values of friction
coefficients are reduced systematically compared to those given in Table 5.3, according
to a general trend expected for fine powders. A reduction on the PP friction coefficients
results in a greater increase in the predicted discharge rate compared to a similar change
104
in the PW friction. Altering both PP and PW friction coefficient results in the most
significant increase in the predicted discharge rate.
Dis
ch
arg
e R
ate
, s
-1
0
200
400
600
800
µs=0.01; µr=0.001
µs=0.01; µr=0.001
µs=0.01; µr=0.001
µs=0.3; µr=0.1
µs=0.7; µr=0.03
µs=0.01; µr=0.001
PP: µs=0.7; µr=0.03
PW: µs=0.3 µr=0.1
CR =0.5
Figure 5.14 Effect of friction coefficient: particle vs. wall interactions; vibration
frequency 240 Hz (Runs 2, 6-8, Table C.1).
5.4.3.3 Static vs. Rolling Friction
Individual effects of changes in static and rolling friction coefficients for PP interactions
on the predicted discharge rate are illustrated in Figure 5.15. A reduction in the PP
coefficient of static friction results in a relatively small increase in the discharge rate.
An increase in the discharge rate is strong when the rolling friction coefficient is reduced
from 0.003 to 0.001. Somewhat unexpectedly, the discharge rate decreases, when further
reduction in the rolling friction coefficient is considered. Although Figure 5.15 only
shows results for one set of calculations, a qualitatively similar behavior indicating a
105
non-monotonic change in the discharge rate as a function of µr for PP interactions was
observed for different vibration frequencies. D
isch
arg
e R
ate
, s
-1
200
250
300
350
Dis
ch
arg
e R
ate
, s
-1
200
300
400
500
600
PP: µs=0.7
PP: µr=0.003
PP: CR=0.5; µr=0.03
PW: C R=0.5; µs=0.3; µr=0.1
0.07 0.01
PP: CR=0.5; µs=0.07
PW: C R=0.5; µs=0.3; µr=0.1
0.001 0.0001
Figure 5.15 Effect of individual static and rolling friction coefficients for PP interactions;
vibration frequency 240 Hz. (Top: Runs 9-11; Bottom: Runs 12-14, Table C.1).
Sensitivity of the predicted discharge rate to the changes in the PW static and rolling
friction coefficients is illustrated in Figure 5.16. Reduction in both µr and µs for the PW
interaction results in an increase in the predicted discharge rate. The discharge rate is
more sensitive to changes in µs.
106
Dis
ch
arg
e R
ate
, s
-1
400
450
500
550
600
PP: CR=0.5; µs=0.07; µr=0.001
PW: C R=0.5; µs=0.3
PW: µ r=0.1 0.001
Dis
ch
arg
e R
ate
, s
-1
400
450
500
550
600
PW: µs=0.3
PP: CR=0.5; µs=0.07; µr=0.001
PW: C R=0.5; µr=0.1
0.01
Figure 5.16 Effect of individual static and rolling frictions for PW interactions; vibration
frequency 240 Hz. (Top: Runs 13, 15; Bottom: Runs 13, 16, Table C.1).
5.4.4 Sensitivity of DEM Predictions to Particle Size Distribution
Particle size distribution shown in Figure 5.7 was replicated in EDEM using an approach
outlined earlier [125]. The particles were generated in individual size bins. Four bins
were created simultaneously. The model generates particles from all bins randomly
within the defined geometry (hopper), generated particles are allowed to fall down and
settle in the gravitational field. It was observed that the particles of different sizes created
by the code mixed uniformly while settling down in the hopper. Color coded images of
the particles initially packed in the hopper were taken with the particles colored based on
their sizes. It was clearly observed that differently sized particles were mixed
107
homogenously. The vibration of the hopper was started only after the particles were
completely settled.
It was observed that even a very narrow particle size distribution accounted for in
the DEM, results in a substantial change in the predicted discharge rate, as shown in
Figure 5.17. Similarly to Figure 5.17, a reduced discharge rate was predicted when
particle size distribution was accounted for while other process parameters were varied,
including vibration amplitude, frequency, and friction coefficients.
Dis
ch
arg
e R
ate
, s
-1
0
200
400
600
800
120Hz 240Hz
PP, PW: C R=0.5; µs=0.01; µr=0.001
Monodisperse
Polydisperse
Figure 5.17 Effect of using a size distribution on the discharge rate (Runs 2, 17-19,
Table C.1).
5.4.5 Sensitivity of DEM Predictions to the Vibration Amplitude
Amplitudes of vibrations measured using photographs of the exit tube were determined
with a finite accuracy (see Table 5.2). The expected effect of the error in the measured
vibration amplitude on the predicted discharge rate is shown in Figure 5.18. For both 120
108
and 500 Hz vibrations, an increase in the vibration amplitude results in an increase in the
predicted discharge rate. Conversely, at 240 Hz, an increase in the amplitude causes a
reduction in the discharge rate. It also appears that the sensitivity to the vibration
amplitude is greatest for the 240 Hz case.
Vibration amplitude, mm
0.10 0.15 0.20 0.25 0.30
Dis
ch
arg
e R
ate
, s
-1
0
100
200
300
400
500
600
700
120 Hz
240 Hz
500 Hz
Figure 5.18 Sensitivity of different frequencies to change in amplitude. (Runs 1, 20, 21,
in Table C.1)
5.4.6 Sensitivity of DEM Predictions to the Type of Vibratory Motion
As mentioned previously, two types of vibratory motions were tested. The first is a single
sinusoidal oscillation and the second is a modulated wave obtained as a superposition of
two sinusoidal vibrations. Discharge rates from the models obtained for these two
situations are presented in Figure 5.19. All these simulations were performed with 5000
poly-dispersed particles using the friction and restitution data listed in Table 5.3. Further
details can be found in Table C.1.
109
Frequency, Hz
Dis
ch
arg
e R
ate
, s
-1
0
100
200
300
400
120 240 500
EDEM 1 sine wave
EDEM complex wave
Figure 5.19 Effect of using a single size wave vs. a modulated wave on discharge rate.
(Runs 22- 27 in Table C.1)
Using a modulated wave results in a slight increase in the discharge rate for 240
Hz and in a more substantial increase for both 120 and 500-Hz vibrations. Thus, using a
modulated wave in DEM appears to be significant when the actual experimental
conditions should be represented accurately.
5.5 Particle Interaction Parameters for Zirconia Beads
The appropriate interaction parameters should enable one to match the observed and
predicted discharge rates for different vibration frequencies used. Based on the analysis
presented in the previous section, it is concluded that poly-disperse powder should be
considered in the model. Effect of the modulation is not negligible and a modulated
wave should be employed by DEM for the final comparisons with experiments. It was
also observed that both PP and PW interaction parameters are essential and need to be
adjusted separately. Effect of each of the interaction parameters on the predicted
110
discharge rate was addressed in detail above for the vibration at 240 Hz. Because these
effects may be different for different vibration frequencies, each frequency must be
considered separately. Details of all computations performed in this study are given in the
appendix, Table C.1, and the results are summarized in Table 5.4. It is remarkable that all
parameters, including coefficient of restitution and both static and rolling coefficients of
friction may affect the discharge rate in either proportional or inverse way, depending on
frequency. Note that a limited range of parameter variation was considered, as shown in
Table 5.4.
Table 5.4 Qualitative Effect of Change in Interaction Parameters on the Discharge Rate
at Different Vibration Frequencies
Interaction Parameter Frequency, Hz
120 240 500
PP 0.50<CR<0.75 Proportional↑ Proportional↑ Inverse↓
0.07<µs<0.7 Inverse↓ Weak Inverse↓
0.003<µr<0.03 Inverse↓ Inverse↓ Proportional↑
PW 0.50<CR<0.75 Proportional↑ Proportional↑ Inverse↓
0.03<µs<0.3 Weak Inverse↓ Proportional↑
0.01<µr<0.1 Inverse↓ Weak Proportional↑
Using findings shown in Table 5.4 as a guideline, the values of interaction parameters
were selected to achieve the closest match with the experimental data, as shown in
Figure 5.20. In these calculations, 5000 poly-disperse particles and modulated amplitude
vibration were considered. Considering the experimental errors, the fine tuning of the
values of CR, µs, and µr for both PP and PW interactions was not attempted; instead, an
111
approximate range of values was found for each parameter that enabled us to approach
the experimental data for all frequencies simultaneously. The results are shown in
Figure 5.20. Experimental data are compared to predictions obtained using the restitution
and friction coefficients shown in Table 5.3 and newly identified friction coefficients
enabling a better match with experiments.
Dis
ch
arg
e R
ate
, s
-1
0
200
400
600
800
Frequency, Hz
120 240 500
Experiment
Parameters from Table 3
PP: CR=0.9; µs=0.7 µr=0.001
PW: CR=0.9; µs=0.01 µr=0.001
Figure 5.20 Effect of change in individual parameters for different frequencies (Runs
25-30 in Table C.1). The legend shows the values of friction and restitution coefficients.
Finally, the effect of the total number of particles on the simulation results is
illustrated in Figure 5.21. Instead of 5000 particles used in preliminary calculations,
20,000 particles were used for the final comparisons of the experimental and predicted
discharge rates. It is observed that the match improves further when a greater number of
particles are used. However, the effect of the number of particles is relatively weak,
112
supporting the present observations of a relatively consistent discharge rate throughout
the experiment, while the amount of powder in the hopper was decreasing.
120 240 500
Frequency, Hz
0
200
400
600
800
Dis
ch
arg
e R
ate
, s-1 Experiment
EDEM 5000 Particles
EDEM 20000 Particles
Figure 5.21 Discharge rate for different frequencies conducted using a modulated wave.
Effect of using a higher number of particles is shown. Runs 28-33 Table C.1).
5.6 Discussion
It is possible that the trends identified here for the effects of different interaction
parameters on the discharge rate or, more generically, on the dynamics of particular
motion, may change if powders of different materials are considered. It is most likely that
the changes in the predicted discharge rate for different particle size distribution,
vibration modulation, and amplitude are mostly affected by the type of powder motion.
In all cases, it is clearly established that neglecting to account for either of the considered
parameters would cause gross errors in the DEM-predicted powder flow. It is particularly
interesting that using an even very narrow particle size distribution changes the results
critically, making it possible to match the experiment, compared to the calculation with
the uniform particle sizes over-predicting the discharge rates substantially.
113
It is not surprising that changes in both restitution and friction coefficients for the
PP interactions affect the predicted discharge rate stronger than comparable changes in
the PW interaction parameters. Based on the number of interactions, PP interactions
dominate and this domination becomes more significant for greater numbers of particles.
Considering that the relative particle velocities in the present calculations and
experiments are low (Figure 10 and Figure 11), the high value of CR=0.9 required to
match the calculations and experiment appears to support an inverse relationship between
CR and the particle velocity proposed in the literature [103, 107, 108].
The observed effect of friction coefficients on the discharge rate for the high
frequency oscillation (500 Hz) is surprising for the cases when an increase in the friction
coefficient results in an increase in the discharge rate (Table 5.4). Similarly surprising is a
reduction in the predicted discharge rate for very low coefficients of rolling friction for
the PP interactions, as shown in Figure 5.15. Qualitatively, it may be proposed that there
are situations when low friction and associated inefficient energy dissipation among
moving powder particles slow down their re-distribution in the hopper. On the other
hand, particle packing needs to be continuously re-adjusted in order to allow a flow of
particles.
114
5.7 Conclusions
The most significant outcomes of the present work are an illustration of the importance of
different simulation parameters on the accuracy of the DEM representation of a powder
flow, and a methodology combining a small scale experiment and its DEM description
enabling one to identify the appropriate interaction parameters for powder systems. The
experiment uses a miniature vibrating hopper and can be applied to characterize the
powder flow for different powders with varied compositions and particle size
distributions.
It is shown, in particular, that all six interaction parameters, including coefficients
of restitution, rolling and static friction characterizing both particle-particle and
particle-wall interactions must be carefully selected. The values of these parameters for
powders are generally not the same as those established for macroscopic bodies. One
exception identified in this work for zirconia beads is the static friction coefficient for
particle-particle interactions, which appears to closely match that used for larger zirconia
spheres.
It is shown that the effect of different interaction parameters on the powder flow
may be both direct and inverse, depending on the vibration frequency. For zirconia
powder fed in a brass hopper, it is established that CR=0.9 and µr=0.001 for both PP and
PW interactions. The values of µs are 0.7 and 0.01, for the PP and PW interactions,
respectively.
115
In addition to selecting the appropriate friction and restitution coefficients, it is
shown that considering a realistic particle size distribution in DEM affects the
calculations substantially. Weaker, but not negligible effects are established for the
vibration amplitude, accounting for the modulation of the vibratory motions, and for
using a realistic number of interacting particles.
116
CHAPTER 6
CONCLUSIONS AND FUTURE WORK
6.1 Conclusions
In the first segment of this thesis, a scale-up model was developed based on the concept
of milling dose, which is defined as the ratio of the energy transferred to the powder from
the milling tools to the mass of the milled powder. This concept has been shown to be
able to provide a universally useful description of the milling progress, irrespective of
devices and milling conditions. Importantly, the energy transfer by both impact and
friction must be considered. To account for the friction, both sliding and rolling
motions of the milling balls in which the energy is transferred to the material being
milled must be considered. The DEM-calculated rate of energy dissipation multiplied
by the experimental milling time enables one to calculate the energy transferred to the
powder from the milling tools. This energy directly determines the material refinement.
Once it is found for a material prepared in a specific milling configuration, it can be used
for predicting milling time required to prepare that material using a new milling device or
altered milling conditions.
For a useful and accurate description of the milling process in DEM,
experimentally validated values for restitution and friction coefficients are necessary.
Both static and rolling friction coefficients were obtained comparing simple experiments
117
with powder-coated milling balls rolling inside the milling vial. The same experiment
was directly modeled by DEM. A comparison of the experimental and observed ball
motion patterns enabled us to determine the appropriate friction coefficients.
The DEM calculations for shaker and planetary mills were found to be accurate.
However, the energy dissipation predicted by the attritor DEM model was much higher
than expected. It was discovered that the calculated energy dissipation in this device
included contribution from events with abnormally high forces, which were a result of
breaking jams occurring inside the mill. Such jamming of the milling media and its
subsequent release resulted in high forces in the model stemmed from the constant rate of
the impeller’s rotation. The magnitudes of the predicted forces were not realistic.
Hence, it was proposed to filter out such high-force, long duration events from further
analysis of powder refinement in the attritor mill. After this filtering, a much better
correlation of the experimentally achieved powder refinement and DEM predictions was
obtained. Subsequently, the milling dose calculated for all three milling devices became
comparable to each other and the validity of the developed scale-up approach was
established.
In the process of validation of the scale-up model, extensive experiments were
conducted which were used as indicators of milling progress. In these experiments, the
same powder was prepared in three milling devices, including shaker, planetary, and
attritor mills. Partially milled samples were recovered at regular time intervals and yield
118
strength was measured for each of these samples. The yield strength was treated as a
milling progress indicator, increasing at longer milling times. In the second phase of
this thesis, a distinctive approach to characterize milling progress, which would eliminate
the extensive experimental procedures, was investigated. Subsequently, in-situ
measurements of such parameters as power, torque, etc., readily quantifiable during the
milling, were identified as a potential replacement for the extensive sample
characterization efforts and thus, indicators of material refinement.
Metal-matrix-composites were found to be suitable candidates to pursue this
study. As an authentication, changes in structural and mechanical characteristics of these
materials prepared by mechanical milling recovered at different milling times were
compared to changes in the parameters characterizing milling process in real time. It was
discovered that before utilizing this procedure for tracking milling progress, it is essential
to know the hardness of the material being milled relative to the milling media. For the
material with components softer than the milling media, increasing yield strength, and
structural refinement directly correlated with increasing motor power, torque, as well as
with increase in the amplitudes of rapid oscillations of all milling process parameters. For
the material with a starting component harder than the milling media, the abrasive action
of the harder starting particles (becoming less significant at longer milling times) affected
the motor power and torque stronger than the hardening of the prepared composite.
119
Overall, changes in the milling process parameters measured in real time were
found useful in tracking the milling progress, although the reduction in the power and
torque (as opposed to their increase) correlated with the material refinement. This
technique was found to be quite effective and even minute changes in morphology such
as the formation of flakes at early milling times could be correlated with real time
measurements.
During the initial development of scale-up model, it was reported that the attritor
mill model resulted in substantially high force events as a result of the jamming events
inside the model. In actual experiments, such jamming events indeed occur, however the
motor develops an appropriate response, which provides an additional torque for the
impeller to overcome the jam. Replicating such a “responsive” impeller in DEM was the
objective of the third portion of this thesis.
It is shown that in the model, the rotation of such “responsive” impeller can be
described using an experimentally obtained correlation between instantaneous values of
torque and rotation rate. This correlation can be programmed into DEM to describe the
torque applied to the impeller for the range of rotation rates observed experimentally.
When the rotation rate falls below the experimental range, the torque needs to be further
increased. The accuracy of DEM representation of material processing in an attritor is
significantly improved when interactions of the moving impeller and the milling balls are
accounted for by enabling the impeller to instantaneously slow down when the balls jam,
120
and then return to its pre-set rotation rate. The performance of this responsive impeller
was tested with different materials, and it was found to accurately predict the energy
dissipation rate or power for all programmed cases. Hence, this advance model aids in
eliminating the superficial filtering process that had to be conducted initially in the
scale-up model development.
The final chapter in this thesis focuses on development of a novel methodology
for identification of friction and restitution coefficients for particle-scale DEM studies.
The lack of appropriate values for such coefficients is a major omission in existing
research utilizing DEM descriptions to understand various unit operations. A miniature
vibratory hopper feeder was developed and used to feed several fine spherical powders.
The hopper was directly described in DEM. In calculations, sensitivity of the DEM
predictions to selection of different interaction parameters, using mono-disperse vs.
poly-disperse powder models, accurately representing vibration pattern and amplitude
were quantified. Further, comparing experimental and predicted powder discharge
rates, appropriate values of coefficients of restitution and friction were established for
both particle-particle and particle-wall interactions. The developed approach combining
miniature hopper experiment and its DEM description can be used in the future to
characterize interaction parameters for different fine powders.
121
6.2 Future Work
A few suggestions for future directions that could be pursued based on the investigation
and outcomes from this thesis are presented in this final section.
In the initial development of the scale-up model, experimental validation was
achieved via tracking the mechanical as well as structural properties of the prepared
non-reactive composites. In addition to this, perhaps advanced reactive materials could be
prepared and characterized with the same intent, to further establish the modeling
approach. In addition to the transfer of manufacturing from one device to another or
small to large scale, a model based on study of reactive materials could potentially even
serve as a way of prediction of “safe” manufacturing conditions for such materials.
The use of in-situ, real-time indicators of milling refinement was focused on the
attritor mill in this thesis. Taking this study forward, such an indicator could perhaps be
also obtained in the planetary and shaker mill. The author recommends temperature
monitoring as one of the ways to accomplish this goal.
An important shortcoming was encountered during the real-time milling progress
assessment for materials milled at cryogenic temperatures. For these materials, it was
observed that the power, torque and variations thereof remained essentially constant
during the entire milling duration (around 24 hours). Details of these measurements are
provided in the appendix. Hence, it was not possible to predict powder morphological
changes and milling behaviors for cryogenically milled samples as exhibited for powders
122
milled at room temperature (Chapter 3). This is an important concern since some of the
sensitive materials can currently be prepared in laboratory scale only under cryogenic
temperatures. Reasons for the incompetence of current real time parameters for such
materials as well as other non-invasive monitoring techniques need to be explored.
Although the current work as well as all the other modeling approaches reported
in literature contribute towards a better understanding of the ball-milling process itself, it
would be interesting to consider a “dynamic” model as opposed to the a “steady-state”
one. It is a known fact that powders undergo welding, fracture and agglomeration as
milling progresses. In this thesis, the morphological transitions were also shown via
real-time measurements in collaboration with scanning electron microscope images of
partially milled samples. When these modifications happen, the properties of the milled
samples in terms of hardness, cohesivity, etc., are rapidly changing. The thickness of
coating on the milling media is rapidly changing as well. Thereby, the interaction
parameters (friction, restitution coefficients) of the milling media are modified with time.
Having said that, the possibility of developing a model, which contains “dynamic”
parameters such that it can perhaps account for the variations the powders go through
inside the mill with time, is most fascinating. It can be contemplated that an advanced
model of this nature would perhaps contain time sensitive interaction and physical
properties. In fact, another varying factor could be the force model itself. In all of the
presented results, the Hertz-Mindlin force model was utilized. In literature, it has been
123
presented to run a more advanced and effective calculation than the linear spring dashpot
model and hence, was a straightforward choice. However, if one considers the
development of a dynamic model, then a transition from simplistic force model to a
model including cohesion or even electrostatics-incorporated case could be considered.
In literature, a few reports were found that boast of a better calculation in DEM
when a velocity dependent restitution coefficient is used. Some of these works were cited
in Chapter 5 of this thesis. The motivation for these studies came from one of the primary
caveats in the existing Hertz-Mindlin model, which is the factor deciding the end of
contact. In the current Hertz-Mindlin model, a contact ends when the displacement
returns to zero and this results in a net normal attractive force at the end of a contact. The
current argument is that contact, in fact, should end when the force returns to zero and not
the displacement. A few authors [126-128] have therefore presented the need for a
velocity-varying coefficient of restitution. However, all of the numerical developments
are based on two-body collisions and it appears that the problem of multiple body
collisions and resulting mathematical problem of varying velocities and restitution
coefficients has not been solved yet. This could result in an extensive study if pursued
and would be quite a valuable contribution to multi-body simulation studies.
During the operation of the attritor mill, the entire vial-cooling jacket assembly
was also observed to wobble at the instances where the impeller “responses” to potential
jamming conditions. Such a “responsive” vial was not incorporated in the current study
124
and it would be interesting to see the outcomes of such a model. It is anticipated that
maybe that would make the model outcomes even better and improve the milling dose
comparisons.
For preparation of advanced materials with tailored particle sizes, a unique
two-step milling methodology was recently developed in this research group [129]. In
such an approach, the samples are first milled under one set of milling conditions and the
resultant materials are then subjected to a different set of conditions (in the same device).
It would be quite interesting to think about how such a process could be effectively
modeled in DEM such that appropriate scale-up parameters can be obtained.
125
APPENDIX A
REAL-TIME INDICATORS OF MILLING PROGRESS:
CRYOGENIC SYSTEMS
The real-time milling progress indicators for two cryogenic temperatures are presented.
The left and right groups presented in Figure A.1 carry no specific reason.
0 5 10 15 20 25
Milling time, Hrs
Po
we
r, W
100
110
120
To
rqu
e,
Nm
2
3
4
5
rpm
406
408
410
5 10 15 20 25
Milling time, Hrs
Al-Wax
Al-Polyethylene
Al-Iodine
Al-Hexane
Al-Magnesium
Figure A.1 Real-time measurements of impeller rotation speed, torque and power for five
systems. The average and standard deviations are shown.
126
APPENDIX B
EFFECT OF HARD-SOFT COMPONENTS IN ATTRITOR MILL PROCESSING
In chapter 3, the effect of powders being harder or softer than milling media was
discussed. Another system is added to the same comparison and characterization results
are presented here.
Table B.1 List of Hardness Values for Materials
Pe
ak w
idth
,
de
gre
es
0.3
0.4
0.5
Milling time, hrs
0 1 2 3 4 5 6
Yie
ld s
tre
ng
th,
MP
a
0
100
200
Al.B4C
Al.SiO2
Al.MgO
Figure B.1 Comparison of experimental milling time indicators for three material
systems.
127
0 1 2 3 4 5 6
Milling time, Hrs
Po
we
r, W
95
110
125
140
To
rqu
e,
Nm
2.5
3.5
4.5
5.5
Al.B4C
Al.SiO2
Al.MgO
Figure B.2 Comparison of real time milling progress indicators for three material
systems.
128
APPENDIX C
DETAILED LIST OF ALL PERFORMED SIMULATIONS
Table C.1 Detailed List of all Performed Simulations in Chapter 5
CR µs µr CR µs µr
1 0.05 0.01 0.001 0.05 0.01 0.001 240 M 20000 Sin 640
2 0.5 0.01 0.001 0.5 0.01 0.001 240 M 20000 Sin 770
3 0.95 0.01 0.001 0.95 0.01 0.001 240 M 20000 Sin 1540
4 0.95 0.01 0.001 0.05 0.01 0.001 240 M 20000 Sin 830
5 0.05 0.01 0.001 0.95 0.01 0.001 240 M 20000 Sin 700
6 0.5 0.7 0.03 0.5 0.3 0.1 240 M 20000 Sin 300
7 0.5 0.01 0.001 0.5 0.3 0.1 240 M 20000 Sin 520
8 0.5 0.7 0.03 0.5 0.01 0.001 240 M 20000 Sin 330
9 0.5 0.7 0.03 0.5 0.3 0.1 240 M 20000 Sin 300
10 0.5 0.07 0.03 0.5 0.3 0.1 240 M 20000 Sin 320
11 0.5 0.01 0.03 0.5 0.3 0.1 240 M 5000 Sin 330
12 0.5 0.07 0.003 0.5 0.3 0.1 240 M 5000 Sin 370
13 0.5 0.07 0.001 0.5 0.3 0.1 240 M 5000 Sin 510
14 0.5 0.07 0.0001 0.5 0.3 0.1 240 M 5000 Sin 450
15 0.5 0.07 0.001 0.5 0.01 0.1 240 M 5000 Sin 590
16 0.5 0.07 0.001 0.5 0.3 0.001 240 M 5000 Sin 520
17 0.5 0.01 0.001 0.5 0.01 0.001 120 M 5000 Sin 250
18 0.5 0.01 0.001 0.5 0.01 0.001 120 P 5000 Sin 120
19 0.5 0.01 0.001 0.5 0.01 0.001 240 P 5000 Sin 370
20 0.5 0.7 0.03 0.5 0.3 0.1 120 M 5000 Sin 50
21 0.9 0.7 0.03 0.9 0.3 0.1 500 P 5000 Sin 150
22 0.5 0.7 0.03 0.5 0.3 0.1 120 P 5000 Sin 40
23 0.5 0.7 0.03 0.5 0.3 0.1 240 P 5000 Sin 290
24 0.5 0.7 0.03 0.5 0.3 0.1 500 P 5000 Sin 180
25 0.5 0.7 0.03 0.5 0.3 0.1 120 P 5000 Mod 60
26 0.5 0.7 0.03 0.5 0.3 0.1 240 P 5000 Mod 300
27 0.5 0.7 0.03 0.5 0.3 0.1 500 P 5000 Mod 210
28 0.9 0.7 0.001 0.9 0.01 0.001 120 P 5000 Mod 100
29 0.9 0.7 0.001 0.9 0.01 0.001 240 P 5000 Mod 630
30 0.9 0.7 0.001 0.9 0.01 0.001 500 P 5000 Mod 150
31 0.9 0.7 0.001 0.9 0.01 0.001 120 P 20000 Mod 120
32 0.9 0.7 0.001 0.9 0.01 0.001 240 P 20000 Mod 670
33 0.9 0.7 0.001 0.9 0.01 0.001 500 P 20000 Mod 170
AmplitudeDischarge
rate, #/sSl #
Particle-Particle Particle-Wall Frequency,
HzParticles
Number of
particles
Legend:
CR: Coefficient of Restitution, µs: Static friction, µr: Rolling friction, M: Mono-disperse,
P: Poly-disperse, Sin: Sinusoidal wave, Mod: Modulated wave
129
APPENDIX D
ALUMINUM-TITANIUM SYSTEM STUDY FOR MILLING PROGRESS
Instead of the Aluminum-Magnesium Oxide results presented in Chapter 2, the study was
initially done with Aluminum-Titanium (composition Al0.8Ti0.2). The results are shown
here.
Table D.1: Milling Parameters for Aluminum Titanium System
Attritor
Powder load, g 50 50 100
Charge ratio 36 3 3
Ball mass, g 1800 150 300
Planetary
MillParameter
Duration, h
0 2 4 6 8 10 120.0
0.2
0.4
0.6
0.8
1.0
Inte
gra
l W
idth
, 2
o
AM_50g_36deg
PM_50g_36deg
PM_100g_36deg
Pure Titanium
Figure D.1 Peak width data for Al-Ti prepared in different devices.
130
APPENDIX E
FRICTION COEFFICIENT RESULTS
This section presented the results of single-ball rolling experiments to obtain friction
coefficients for systems not shown in the main chapters in this thesis.
Table E.1 Friction Coefficient Processing Results
Static Rolling
Plain N/A Plain ball on plain vial 0.28 0.0075
Coated ball 0.17 0.02
Highly coated ball 0.1 0.01
8 hours Coated ball 0.25 0.032
Wet milling, 8AlMoO3 15 min Coated ball 0.1 0.09
Friction CoefficientRun Milling Duration Case
Dry milling, Al.Ti
2 hours
131
APPENDIX F
AMPLITUDE RESULTS DETAILS
The amplitudes discussed in Chapter 5 were measured by monitoring both top and
bottom position of the hopper tip. Detailed outcomes are shown in the following plot.
Po
sitio
n, m
m
-0.30
-0.25
-0.20
-0.15
-0.10
-0.05
Po
sitio
n, m
m
-0.20
-0.15
-0.10
-0.05
0.00
Frame, #
1 2 3 4 5
Po
sitio
n, m
m
-0.05
0.00
0.05
0.10
0.15
0.20
Bottom
Top
120Hz
240Hz
500Hz
Figure F.1 Amplitude data calculated at each frame for different frequencies.
132
APPENDIX G
ADDITIONAL RESULTS FOR DIFFERENT MATERIAL SYSTEMS
(ADDENDUM TO CHAPTER 5)
The experiments discussed in Chapter 5 for Zirconia were also performed for two other
materials: PMMA and Titanium. The respective characterization and hopper discharge
rate results are presented in this appendix.
Figure G.1 SEM Images of the three material systems.
The particle size distributions for these materials are shown in Figure G.2. The outcomes
for Zirconia and PMMA were obtained by image processing of SEM images (as
described in Chapter 5). 323 and 217 particles were processed for Zirconia and PMMA
respectively. The distribution for Titanium was obtained from a LS-230 Coulter device.
This Titanium is manufactured by Super Conductors Inc. and the presented distribution
was obtained after sieving the sample.
133
0
50
100
150
200
Nu
mb
er
of p
art
icle
s
0
50
100
150
200PMMA
Manufacturer Specs: Avg. Diameter= 49m
Diameter, m
30 40 50 60 70 80 90 1000
50
100
150
200Titanium
Manufacturer Specs: Avg. Diameter= 63m
ZirconiaManufacturer Specs: Avg. Diameter= 50m
Figure G.2 Particle size distribution for the three cases.
Hopper discharge rates are shown in Figure G.3 and the percentage exited in Figure G.4.
134
Frequency, Hz
Dis
ch
arg
e R
ate
, s
-1
0
200
400
600
800
1000
1200
1400
120 240 500 1000
PMMA
Zirconia
Titanium
Figure G.3 Discharge rate comparisons for various cases.
Frequency, Hz
0
20
40
60
80
100
Pe
rce
nta
ge
Exite
d, %
120 240 500 1000
PMMA
Zirconia
Titanium
Figure G.4 Percentage mass exited at different frequencies for the three material
systems.
Initially, when the PMT was set-up in these experiments, it was anticipated that the peak
voltages measured for each particle could be used to interpret the particle sizes being
discharged as well. Although this particular study was not pursued later, the results of the
135
peak voltages (obtained by processing of PMT pulses) for the three particle systems are
shown in Figure G.5. The number of particles (or peaks) processed for each case are
shown in the insets.
0
10
20
30
Titanium262 particles
Zirconia198 particles
0
10
20
30
Voltage, V
0 2 4 6 8 10
Nu
mb
er
of p
ea
ks
0
10
20
30
PMMA185 particles
Figure G.5 Histograms of the measured voltage peaks for the three materials.
136
APPENDIX H
TRANSFER OF PARAMETERS FROM PLANETARY TO ATTRITOR:
IN-SITU MEASUREMENTS
Both real time and experimental milling progress indicators are shown in Figure H.1.
To
rqu
e
sta
nd
ard
de
via
tio
n
0.0
0.4
0.8
Ave
rag
e
to
rqu
e
2.0
2.5
3.0
3.5
Po
we
r
sta
nd
ard
de
via
tio
n
0
2
4
6
8
10
0.0 1.0 2.0 3.0 4.0
Milling time, hrs
40
70
100
Yie
ld s
tre
ng
th,
MP
a
Attritor_400rpm
AM_200rpm
PM_300rpm
Figure H.1 Comparison of experimental and real-time milling progress indicators for
transfer of sample from planetary to attritor mill. (powder mass is 50g).
137
After preparing the sample in planetary mill, the milled material was transferred to an
attritor and the impeller rotation was initiated.
Here, the values of real time indicators for this powder (from planetary mill) were
recorded. The usability of real-time indicators is further established here as we observe
the planetary mill real time data is similar to where the experimental trends are.
138
APPENDIX I
RESULTS FOR LARGER ATTRITOR VIALS
Some experiments and EDEM calculations were performed with larger (1400cc) steel
and ceramic vials. The corresponding results are presented in this appendix. The
experimental results are limited for the larger vials and the reasons for the lack of data are
different for steel and ceramic vials. A motor overload was observed in the ceramic vial,
Perhaps this was caused due to the material of construction of the vial which could not
“respond” or adjust to the jams the way steel vials do. In the case of larger steel vial,
multiple deformations on the vial wall occurred during such jamming responses which
resulted in the vial being stuck in the enclosure at the end of every experiment.
0 1 2 3 4 8
Milling time, hrs
40
50
60
70
80
90
100
110
120
Yie
ld s
trength
, M
Pa
/ /
AM: 400 rpm
AM: 200rpm
AM:200rpm, Ceramic
AM:400rpm:1400cc vial
Figure I.1 Yield strength results for larger ceramic and steel vials relative to smaller
attritor vials.
139
Figure I.2 DEM model of larger ceramic vial.
Inte
ractio
n e
ve
nts
(co
llisio
ns)
100101102103104100101102103104 Attritor:
400 rpm
Attritor: 200 rpm
Filtered out
10-4 10-3 10-2 10-1 100 101 102 103 104 105
Average Force
100101102
103104105
Attritor: 400 rpm1400cc
100
101
102
103
104
105
Attritor: 200 rpm1400cc
Figure I.3 Histograms of events sorted based on average force during the simulation for
smaller and larger vials are depicted.
140
rpm
203.0
203.5
204.0
204.5
205.0
To
rqu
e
1.0
1.5
2.0
2.5
3.0
3.5
1/2 load
Po
we
r
48
50
52
54
56
Just balls Balls+
Hexane1/3 load 1/4 load No powder
No balls
blank
Figure I.4 Results of parametric investigation for ceramic 1400cc vial operated at
200rpm.
141
Ceramic 200rpm1100cc
Po
we
r, W
101
102
103
104
Steel 400 rpm750cc
Steel 200 rpm750cc
Steel 400rpm1400cc
DAS
EDEM Screened
EDEM Raw
Figure I.5 Power data from EDEM and data acquisition for different cases.
142
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